{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,1],[1,1,2],[1,2,1],[2,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[567,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0001","image_path":"images/combination3d_0001.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0001_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0001_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0001_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0001_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0001_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1,"target_cube_count":14,"target_cubes":[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[557,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0002","image_path":"images/combination3d_0002.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0002_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0002_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0002_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0002_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0002_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,2,0],[0,2,1],[1,0,2],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[1,2,2],[1,2,3]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12}],"canvas_size":[580,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0003","image_path":"images/combination3d_0003.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0003_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0003_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0003_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0003_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0003_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":3,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[0,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":8}],"canvas_size":[580,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0004","image_path":"images/combination3d_0004.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0004_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0004_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0004_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0004_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0004_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":4,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[582,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0005","image_path":"images/combination3d_0005.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0005_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0005_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0005_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_0005_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0005_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":5,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":15}],"canvas_size":[560,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0006","image_path":"images/combination3d_0006.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0006_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0006_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0006_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0006_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0006_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":6,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[591,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0007","image_path":"images/combination3d_0007.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0007_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0007_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0007_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0007_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0007_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":7,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,1,0],[3,2,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,2,3],[1,2,4],[2,2,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[579,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0008","image_path":"images/combination3d_0008.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0008_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0008_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0008_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0008_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0008_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":8,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":10}],"canvas_size":[609,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0009","image_path":"images/combination3d_0009.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0009_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0009_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0009_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0009_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0009_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":9,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,3,0],[1,4,0],[1,4,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[1,3,1],[1,4,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,3,0],[1,4,0],[1,4,1],[2,1,0]]],"total_cube_count":12}],"canvas_size":[554,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0010","image_path":"images/combination3d_0010.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0010_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0010_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0010_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0010_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0010_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":10,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[1,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,1],[2,2,0],[2,2,1],[2,3,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":13}],"canvas_size":[607,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0011","image_path":"images/combination3d_0011.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0011_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0011_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0011_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0011_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0011_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":11,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,0,1],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,2],[1,0,2],[1,1,2],[1,2,1],[1,2,2],[2,1,2],[2,2,0],[2,2,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,2,1],[2,3,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,2,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13}],"canvas_size":[610,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0012","image_path":"images/combination3d_0012.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0012_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0012_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0012_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0012_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0012_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":12,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,1,1],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,0,2],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,2],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[583,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0013","image_path":"images/combination3d_0013.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0013_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0013_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0013_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_0013_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0013_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":13,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,4,0],[1,4,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,1],[2,2,1],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[563,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0014","image_path":"images/combination3d_0014.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0014_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0014_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0014_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0014_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0014_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":14,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12}],"canvas_size":[576,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0015","image_path":"images/combination3d_0015.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0015_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0015_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0015_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0015_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0015_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":15,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,2,2],[1,2,2],[2,0,2],[2,1,2],[2,2,0],[2,2,1],[2,2,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0]]],"total_cube_count":11}],"canvas_size":[596,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0016","image_path":"images/combination3d_0016.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0016_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0016_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0016_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0016_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0016_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":16,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,1,2],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[616,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0017","image_path":"images/combination3d_0017.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0017_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0017_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0017_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_0017_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0017_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":17,"target_cube_count":14,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0],[2,3,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,1],[2,3,0],[2,3,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,0,3],[0,1,2],[0,1,3],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,3],[2,1,3]]],"total_cube_count":13}],"canvas_size":[573,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0018","image_path":"images/combination3d_0018.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0018_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0018_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0018_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0018_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0018_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":18,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,4],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[555,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0019","image_path":"images/combination3d_0019.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0019_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0019_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0019_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0019_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_0019_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":19,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[569,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0020","image_path":"images/combination3d_0020.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0020_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0020_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0020_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0020_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0020_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":20,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,3,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[571,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0021","image_path":"images/combination3d_0021.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0021_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0021_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0021_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0021_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0021_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":21,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,3,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[567,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0022","image_path":"images/combination3d_0022.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0022_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0022_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0022_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0022_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0022_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":22,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[587,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0023","image_path":"images/combination3d_0023.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0023_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0023_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0023_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_0023_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0023_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":23,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,0,2],[0,0,3],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[599,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0024","image_path":"images/combination3d_0024.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0024_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0024_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0024_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0024_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0024_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":24,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":15}],"canvas_size":[598,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0025","image_path":"images/combination3d_0025.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0025_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0025_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0025_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_0025_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0025_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":25,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[575,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0026","image_path":"images/combination3d_0026.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0026_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0026_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0026_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_0026_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0026_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":26,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,1]]],"total_cube_count":10}],"canvas_size":[611,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0027","image_path":"images/combination3d_0027.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0027_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0027_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0027_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0027_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0027_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":27,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,2,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[564,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0028","image_path":"images/combination3d_0028.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0028_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0028_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0028_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0028_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0028_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":28,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[620,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0029","image_path":"images/combination3d_0029.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0029_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0029_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0029_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0029_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0029_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":29,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[619,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0030","image_path":"images/combination3d_0030.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0030_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0030_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0030_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0030_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0030_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":30,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,2,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[551,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0031","image_path":"images/combination3d_0031.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0031_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0031_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0031_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0031_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0031_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":31,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[559,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0032","image_path":"images/combination3d_0032.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0032_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0032_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0032_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0032_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0032_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":32,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":10}],"canvas_size":[571,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0033","image_path":"images/combination3d_0033.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0033_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0033_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0033_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0033_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0033_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":33,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[1,2,1],[1,3,0],[1,3,1],[1,4,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1],[2,4,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[617,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0034","image_path":"images/combination3d_0034.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0034_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0034_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0034_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0034_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_0034_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":34,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,2],[1,1,3],[1,1,4],[2,0,0],[2,1,4]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,2],[1,1,3],[1,1,4],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,2],[2,0,1],[2,1,1],[3,0,1],[3,1,1],[4,1,1]]],"total_cube_count":14}],"canvas_size":[620,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0035","image_path":"images/combination3d_0035.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0035_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0035_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0035_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0035_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0035_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":35,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[592,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0036","image_path":"images/combination3d_0036.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0036_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0036_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0036_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0036_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0036_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":36,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13}],"canvas_size":[561,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0037","image_path":"images/combination3d_0037.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0037_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0037_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0037_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0037_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0037_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":37,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,1,1],[1,1,1],[2,0,0],[2,0,1],[2,1,1],[2,1,2],[2,2,1],[2,2,2],[2,3,2],[3,3,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[2,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":15}],"canvas_size":[603,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0038","image_path":"images/combination3d_0038.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0038_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0038_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0038_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0038_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0038_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":38,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[2,0,1],[2,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,2],[2,0,2],[3,0,2]]],"total_cube_count":11}],"canvas_size":[576,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0039","image_path":"images/combination3d_0039.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0039_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0039_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0039_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0039_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0039_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":39,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[0,3,2],[1,0,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,1],[1,1,1],[1,1,3]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[608,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0040","image_path":"images/combination3d_0040.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0040_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0040_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0040_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0040_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0040_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":40,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,1],[2,2,1]]],"total_cube_count":9}],"canvas_size":[598,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0041","image_path":"images/combination3d_0041.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0041_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0041_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0041_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0041_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0041_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":41,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,1,2]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1]],[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1]],[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[564,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0042","image_path":"images/combination3d_0042.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0042_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0042_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0042_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0042_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0042_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":42,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[1,1,2]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]]],"total_cube_count":13}],"canvas_size":[554,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0043","image_path":"images/combination3d_0043.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0043_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0043_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0043_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0043_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0043_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":43,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,1,1],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,3]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,1,2]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12}],"canvas_size":[602,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0044","image_path":"images/combination3d_0044.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0044_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0044_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0044_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0044_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0044_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":44,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[584,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0045","image_path":"images/combination3d_0045.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0045_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0045_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0045_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0045_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0045_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":45,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":8}],"canvas_size":[559,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0046","image_path":"images/combination3d_0046.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0046_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0046_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0046_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0046_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0046_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":46,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[595,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0047","image_path":"images/combination3d_0047.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0047_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0047_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0047_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0047_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0047_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":47,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[4,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":9}],"canvas_size":[620,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0048","image_path":"images/combination3d_0048.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0048_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0048_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0048_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0048_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0048_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":48,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0],[4,1,0],[4,2,0],[4,3,0],[4,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,3],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[558,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0049","image_path":"images/combination3d_0049.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0049_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0049_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0049_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0049_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0049_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":49,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[613,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0050","image_path":"images/combination3d_0050.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0050_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0050_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0050_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0050_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0050_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":50,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[581,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0051","image_path":"images/combination3d_0051.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0051_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0051_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0051_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0051_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0051_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":51,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,1,2],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,2]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[584,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0052","image_path":"images/combination3d_0052.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0052_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0052_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0052_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0052_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0052_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":52,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,3],[0,1,1],[0,1,2],[0,1,3],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":12}],"canvas_size":[577,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0053","image_path":"images/combination3d_0053.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0053_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0053_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0053_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0053_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0053_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":53,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[4,0,0],[4,1,0],[4,1,1],[5,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,3]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[567,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0054","image_path":"images/combination3d_0054.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0054_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0054_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0054_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0054_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0054_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":54,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,3,0],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1]]],"total_cube_count":9}],"canvas_size":[561,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0055","image_path":"images/combination3d_0055.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0055_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0055_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0055_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0055_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0055_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":55,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0],[3,1,0],[4,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,1,0],[4,0,0]]],"total_cube_count":13}],"canvas_size":[551,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0056","image_path":"images/combination3d_0056.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0056_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0056_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0056_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0056_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0056_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":56,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,2],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":12}],"canvas_size":[555,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0057","image_path":"images/combination3d_0057.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0057_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0057_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0057_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0057_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0057_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":57,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[2,3,2],[2,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[3,0,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":14}],"canvas_size":[575,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0058","image_path":"images/combination3d_0058.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0058_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0058_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0058_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0058_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0058_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":58,"target_cube_count":13,"target_cubes":[[0,3,0],[0,3,1],[0,3,2],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],[[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13}],"canvas_size":[578,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0059","image_path":"images/combination3d_0059.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0059_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0059_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0059_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0059_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0059_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":59,"target_cube_count":13,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,2],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,0,1],[1,1,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":12}],"canvas_size":[589,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0060","image_path":"images/combination3d_0060.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0060_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0060_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0060_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0060_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0060_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":60,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,0,2],[3,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,0],[2,0,2]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,2],[0,1,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]]],"total_cube_count":13}],"canvas_size":[613,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0061","image_path":"images/combination3d_0061.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0061_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0061_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0061_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0061_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0061_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":61,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,1],[3,1,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,0],[4,0,0],[4,1,0],[4,2,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,2]]],"total_cube_count":15}],"canvas_size":[572,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0062","image_path":"images/combination3d_0062.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0062_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0062_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0062_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0062_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0062_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":62,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,1,4]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":10}],"canvas_size":[606,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0063","image_path":"images/combination3d_0063.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0063_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0063_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0063_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_0063_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0063_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":63,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[2,0,1],[2,1,0],[2,1,1],[3,0,1],[3,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[610,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0064","image_path":"images/combination3d_0064.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0064_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0064_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0064_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0064_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0064_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":64,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,2],[0,0,3],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":10}],"canvas_size":[603,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0065","image_path":"images/combination3d_0065.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0065_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0065_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0065_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0065_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0065_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":65,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":11}],"canvas_size":[559,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0066","image_path":"images/combination3d_0066.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0066_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0066_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0066_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0066_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0066_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":66,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,2],[0,3,2],[1,2,1],[1,3,1],[1,3,2],[1,3,3],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,1],[1,2,1],[1,2,2],[1,2,3],[2,2,1],[2,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[3,1,1],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[559,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0067","image_path":"images/combination3d_0067.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0067_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0067_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0067_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0067_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0067_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":67,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[3,2,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13}],"canvas_size":[609,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0068","image_path":"images/combination3d_0068.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0068_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0068_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0068_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0068_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0068_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":68,"target_cube_count":13,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[0,3,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[3,1,1],[4,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,1],[3,0,1],[3,1,1],[3,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":15}],"canvas_size":[554,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0069","image_path":"images/combination3d_0069.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0069_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0069_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0069_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0069_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0069_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":69,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14}],"canvas_size":[565,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0070","image_path":"images/combination3d_0070.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0070_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0070_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0070_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0070_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0070_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":70,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0],[3,0,1],[3,0,2],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":12}],"canvas_size":[591,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0071","image_path":"images/combination3d_0071.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0071_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0071_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0071_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0071_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0071_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":71,"target_cube_count":12,"target_cubes":[[0,0,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,4,1],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[1,4,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12}],"canvas_size":[559,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0072","image_path":"images/combination3d_0072.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0072_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0072_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0072_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0072_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0072_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":72,"target_cube_count":12,"target_cubes":[[0,4,0],[0,4,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,3,0],[2,4,0],[2,5,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,3]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":13}],"canvas_size":[585,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0073","image_path":"images/combination3d_0073.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0073_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0073_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0073_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0073_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0073_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":73,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,4,0],[1,4,0],[2,4,0],[2,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0]]],"total_cube_count":9}],"canvas_size":[615,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0074","image_path":"images/combination3d_0074.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0074_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0074_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0074_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0074_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0074_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":74,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11}],"canvas_size":[607,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0075","image_path":"images/combination3d_0075.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0075_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0075_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0075_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_0075_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0075_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":75,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[2,0,1],[2,0,2],[3,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2],[2,0,0],[2,1,0],[2,1,1],[3,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":11}],"canvas_size":[597,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0076","image_path":"images/combination3d_0076.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0076_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0076_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0076_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_0076_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0076_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":76,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[582,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0077","image_path":"images/combination3d_0077.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0077_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0077_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0077_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_0077_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0077_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":77,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,2],[0,1,3],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,2]]],"total_cube_count":10}],"canvas_size":[574,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0078","image_path":"images/combination3d_0078.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0078_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0078_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0078_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0078_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0078_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":78,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[568,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0079","image_path":"images/combination3d_0079.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0079_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0079_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0079_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0079_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0079_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":79,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12}],"canvas_size":[584,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0080","image_path":"images/combination3d_0080.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0080_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0080_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0080_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0080_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0080_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":80,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,0,1],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[0,3,1],[1,2,1],[1,3,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12}],"canvas_size":[614,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0081","image_path":"images/combination3d_0081.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0081_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0081_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0081_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0081_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0081_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":81,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[1,2,2],[2,2,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,3],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[568,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0082","image_path":"images/combination3d_0082.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0082_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0082_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0082_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0082_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0082_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":82,"target_cube_count":11,"target_cubes":[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[3,1,1],[3,2,0],[3,2,1],[3,2,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1],[3,1,1],[3,2,0],[3,2,1],[3,2,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[3,0,2],[3,1,1],[3,1,2],[3,2,2]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":14}],"canvas_size":[613,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0083","image_path":"images/combination3d_0083.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0083_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0083_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0083_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0083_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0083_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":83,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,1,1],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,2,1],[0,2,2],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,1],[2,2,0],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,1,3],[0,2,3],[1,1,2],[1,1,3]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,1],[1,0,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[3,0,1],[3,1,0],[3,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,1,3],[1,1,2],[1,1,3]]],"total_cube_count":14}],"canvas_size":[586,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0084","image_path":"images/combination3d_0084.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0084_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0084_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0084_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0084_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0084_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":84,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":13}],"canvas_size":[575,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0085","image_path":"images/combination3d_0085.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0085_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0085_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0085_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_0085_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0085_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":85,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,0,0],[3,1,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,3]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[1,2,3],[1,3,2],[1,3,3],[2,3,1],[2,3,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1]]],"total_cube_count":14}],"canvas_size":[553,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0086","image_path":"images/combination3d_0086.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0086_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0086_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0086_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0086_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0086_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":86,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[568,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0087","image_path":"images/combination3d_0087.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0087_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0087_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0087_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0087_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0087_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":87,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":10}],"canvas_size":[600,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0088","image_path":"images/combination3d_0088.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0088_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0088_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0088_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0088_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0088_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":88,"target_cube_count":10,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,2],[1,0,0],[1,2,2]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1]],[[0,1,3],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2]]],"total_cube_count":12}],"canvas_size":[560,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0089","image_path":"images/combination3d_0089.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0089_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0089_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0089_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0089_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0089_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":89,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[3,2,0],[4,1,0],[4,1,1],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":9}],"canvas_size":[576,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0090","image_path":"images/combination3d_0090.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0090_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0090_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0090_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0090_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0090_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":90,"target_cube_count":8,"target_cubes":[[0,1,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,2,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,2],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,1]]],"total_cube_count":9}],"canvas_size":[560,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0091","image_path":"images/combination3d_0091.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0091_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0091_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0091_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0091_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_0091_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":91,"target_cube_count":9,"target_cubes":[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,1,0],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[2,0,1],[2,1,1],[3,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0],[4,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[4,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[603,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0092","image_path":"images/combination3d_0092.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0092_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0092_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0092_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0092_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0092_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":92,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2],[3,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[613,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0093","image_path":"images/combination3d_0093.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0093_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0093_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0093_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0093_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0093_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":93,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,2,1],[3,3,0],[3,3,1],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,3,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[1,2,1],[1,3,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2],[0,1,3]]],"total_cube_count":8}],"canvas_size":[619,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0094","image_path":"images/combination3d_0094.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0094_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0094_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0094_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0094_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0094_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":94,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0],[4,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,1],[0,1,2],[0,2,1],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[4,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[0,4,0],[1,0,0],[1,2,1],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[618,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0095","image_path":"images/combination3d_0095.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0095_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0095_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0095_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0095_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0095_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":95,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,2]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,1],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[597,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0096","image_path":"images/combination3d_0096.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0096_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0096_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0096_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0096_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0096_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":96,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,0,5]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2],[3,1,3]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[3,0,0]]],"total_cube_count":14}],"canvas_size":[574,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0097","image_path":"images/combination3d_0097.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0097_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0097_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0097_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0097_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0097_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":97,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[4,0,0],[4,0,1],[4,0,2],[4,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[0,2,3],[0,3,2],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[1,2,2],[1,2,3],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1]]],"total_cube_count":15}],"canvas_size":[595,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0098","image_path":"images/combination3d_0098.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0098_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0098_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0098_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0098_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0098_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":98,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":9}],"canvas_size":[601,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0099","image_path":"images/combination3d_0099.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0099_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0099_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0099_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0099_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0099_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":99,"target_cube_count":9,"target_cubes":[[0,2,0],[1,2,0],[2,2,0],[2,2,1],[2,3,0],[3,2,0],[4,0,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[1,2,2],[2,2,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":11}],"canvas_size":[568,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0100","image_path":"images/combination3d_0100.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0100_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0100_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0100_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0100_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0100_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":100,"target_cube_count":11,"target_cubes":[[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,2],[1,0,2],[1,1,0],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[1,4,0],[1,4,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":12}],"canvas_size":[574,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0101","image_path":"images/combination3d_0101.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0101_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0101_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0101_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0101_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0101_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":101,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1],[2,1,0],[2,2,0],[2,2,1]]],"total_cube_count":12}],"canvas_size":[568,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0102","image_path":"images/combination3d_0102.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0102_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0102_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0102_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0102_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0102_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":102,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[608,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0103","image_path":"images/combination3d_0103.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0103_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0103_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0103_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0103_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0103_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":103,"target_cube_count":13,"target_cubes":[[0,2,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,0,0],[2,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[552,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0104","image_path":"images/combination3d_0104.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0104_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0104_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0104_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0104_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_0104_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":104,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0]],[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,3,1],[2,1,0],[2,1,1],[2,2,1],[3,1,1]]],"total_cube_count":14}],"canvas_size":[594,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0105","image_path":"images/combination3d_0105.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0105_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0105_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0105_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0105_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0105_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":105,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[3,0,1],[3,0,2]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,3,2],[1,1,1],[1,2,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[611,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0106","image_path":"images/combination3d_0106.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0106_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0106_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0106_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0106_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0106_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":106,"target_cube_count":12,"target_cubes":[[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0],[3,1,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,2,1],[1,2,2],[2,0,1],[2,1,1],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12}],"canvas_size":[581,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0107","image_path":"images/combination3d_0107.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0107_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0107_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0107_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0107_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0107_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":107,"target_cube_count":12,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[3,1,2],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[4,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,2,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[566,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0108","image_path":"images/combination3d_0108.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0108_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0108_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0108_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0108_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0108_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":108,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,2]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[585,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0109","image_path":"images/combination3d_0109.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0109_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0109_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0109_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0109_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0109_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":109,"target_cube_count":11,"target_cubes":[[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":15}],"canvas_size":[599,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0110","image_path":"images/combination3d_0110.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0110_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0110_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0110_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0110_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0110_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":110,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,2],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[577,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0111","image_path":"images/combination3d_0111.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0111_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0111_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0111_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0111_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0111_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":111,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[2,1,2]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[611,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0112","image_path":"images/combination3d_0112.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0112_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0112_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0112_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0112_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0112_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":112,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,0,2],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,3],[0,1,3],[0,1,4],[0,2,4],[1,0,3],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[553,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0113","image_path":"images/combination3d_0113.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0113_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0113_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0113_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0113_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0113_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":113,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8}],"canvas_size":[580,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0114","image_path":"images/combination3d_0114.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0114_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0114_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0114_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0114_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0114_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":114,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2],[2,1,1],[3,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":15}],"canvas_size":[586,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0115","image_path":"images/combination3d_0115.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0115_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0115_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0115_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_0115_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0115_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":115,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":10}],"canvas_size":[619,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0116","image_path":"images/combination3d_0116.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0116_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0116_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0116_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0116_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0116_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":116,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[580,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0117","image_path":"images/combination3d_0117.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0117_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0117_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0117_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0117_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0117_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":117,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":8}],"canvas_size":[573,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0118","image_path":"images/combination3d_0118.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0118_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0118_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0118_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0118_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0118_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":118,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0]],[[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,1,2],[1,2,2],[1,2,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[2,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0],[3,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[2,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[2,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13}],"canvas_size":[586,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0119","image_path":"images/combination3d_0119.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0119_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0119_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0119_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0119_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0119_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":119,"target_cube_count":13,"target_cubes":[[0,3,0],[1,3,0],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[4,1,0],[4,2,0],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,1],[2,1,0],[2,1,1],[3,0,1],[4,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[4,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[4,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9}],"canvas_size":[615,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0120","image_path":"images/combination3d_0120.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0120_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0120_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0120_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0120_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_0120_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":120,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,1,0],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[561,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0121","image_path":"images/combination3d_0121.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0121_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0121_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0121_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_0121_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0121_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":121,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":12}],"canvas_size":[615,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0122","image_path":"images/combination3d_0122.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0122_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0122_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0122_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_0122_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0122_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":122,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0],[4,1,0],[4,1,1],[5,0,0],[5,1,0],[5,1,1],[5,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[556,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0123","image_path":"images/combination3d_0123.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0123_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0123_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0123_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0123_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0123_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":123,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8}],"canvas_size":[585,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0124","image_path":"images/combination3d_0124.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0124_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0124_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0124_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0124_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0124_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":124,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[0,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,2,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,3],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,2],[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,3,1],[1,3,2],[2,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":15}],"canvas_size":[581,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0125","image_path":"images/combination3d_0125.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0125_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0125_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0125_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0125_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_0125_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":125,"target_cube_count":14,"target_cubes":[[0,2,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[3,3,0],[3,3,1],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,3],[0,2,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":12}],"canvas_size":[557,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0126","image_path":"images/combination3d_0126.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0126_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0126_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0126_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0126_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0126_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":126,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,1,2],[1,2,0],[1,2,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,2,1],[1,2,2],[1,2,3]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[555,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0127","image_path":"images/combination3d_0127.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0127_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0127_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0127_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0127_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0127_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":127,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,4,1],[2,2,0],[2,4,0],[2,4,1],[2,4,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12}],"canvas_size":[580,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0128","image_path":"images/combination3d_0128.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0128_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0128_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0128_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0128_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0128_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":128,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[616,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0129","image_path":"images/combination3d_0129.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0129_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0129_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0129_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0129_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0129_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":129,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,2,0],[3,2,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":10}],"canvas_size":[616,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0130","image_path":"images/combination3d_0130.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0130_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0130_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0130_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0130_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_0130_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":130,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,1],[2,0,2],[2,0,3],[2,1,1],[2,1,2],[3,0,1],[3,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":14}],"canvas_size":[590,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0131","image_path":"images/combination3d_0131.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0131_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0131_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0131_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0131_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0131_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":131,"target_cube_count":14,"target_cubes":[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2],[2,1,1],[2,1,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11}],"canvas_size":[602,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0132","image_path":"images/combination3d_0132.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0132_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0132_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0132_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_0132_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0132_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":132,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[613,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0133","image_path":"images/combination3d_0133.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0133_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0133_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0133_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0133_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0133_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":133,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,1,0],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[611,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0134","image_path":"images/combination3d_0134.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0134_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0134_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0134_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0134_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_0134_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":134,"target_cube_count":9,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":13}],"canvas_size":[597,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0135","image_path":"images/combination3d_0135.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0135_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0135_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0135_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0135_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0135_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":135,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[604,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0136","image_path":"images/combination3d_0136.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0136_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0136_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0136_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0136_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0136_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":136,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,3,0],[1,4,0],[1,4,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,3,0],[2,4,0],[2,4,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,3],[0,1,4],[1,0,2],[1,1,4]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11}],"canvas_size":[559,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0137","image_path":"images/combination3d_0137.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0137_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0137_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0137_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0137_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0137_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":137,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,3,0],[1,4,0],[1,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1]],[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[2,0,0]],[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":12}],"canvas_size":[574,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0138","image_path":"images/combination3d_0138.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0138_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0138_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0138_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0138_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0138_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":138,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[4,1,0],[5,0,0],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12}],"canvas_size":[550,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0139","image_path":"images/combination3d_0139.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0139_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0139_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0139_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0139_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0139_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":139,"target_cube_count":12,"target_cubes":[[0,2,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[3,2,2],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,1],[3,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[562,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0140","image_path":"images/combination3d_0140.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0140_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0140_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0140_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_0140_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0140_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":140,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9}],"canvas_size":[616,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0141","image_path":"images/combination3d_0141.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0141_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0141_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0141_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_0141_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0141_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":141,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,1],[1,0,1],[1,0,2],[2,0,0],[2,0,1]]],"total_cube_count":11}],"canvas_size":[612,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0142","image_path":"images/combination3d_0142.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0142_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0142_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0142_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0142_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0142_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":142,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[573,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0143","image_path":"images/combination3d_0143.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0143_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0143_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0143_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0143_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0143_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":143,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,1,1],[1,2,1],[1,3,1],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[2,0,1],[2,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[607,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0144","image_path":"images/combination3d_0144.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0144_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0144_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0144_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0144_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0144_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":144,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[604,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0145","image_path":"images/combination3d_0145.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0145_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0145_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0145_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0145_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0145_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":145,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,2,1],[0,3,1],[0,4,1],[1,0,1],[1,1,1],[1,2,1],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,1],[1,1,2],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[567,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0146","image_path":"images/combination3d_0146.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0146_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0146_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0146_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0146_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0146_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":146,"target_cube_count":12,"target_cubes":[[0,2,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,0,2]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":11}],"canvas_size":[569,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0147","image_path":"images/combination3d_0147.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0147_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0147_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0147_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0147_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0147_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":147,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,4],[0,0,5],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[1,1,3],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,4,0],[0,5,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[1,4,0],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,2],[0,2,3],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,2]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,4,0],[0,5,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[601,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0148","image_path":"images/combination3d_0148.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0148_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0148_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0148_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_0148_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0148_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":148,"target_cube_count":13,"target_cubes":[[0,4,0],[0,5,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,2],[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[559,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0149","image_path":"images/combination3d_0149.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0149_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0149_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0149_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0149_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0149_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":149,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,1,1],[3,1,2],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[591,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0150","image_path":"images/combination3d_0150.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0150_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0150_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0150_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0150_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0150_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":150,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,3],[1,1,3],[2,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[602,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0151","image_path":"images/combination3d_0151.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0151_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0151_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0151_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0151_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0151_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":151,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,2,2],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[600,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0152","image_path":"images/combination3d_0152.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0152_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0152_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0152_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0152_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0152_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":152,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[3,1,0],[3,1,1],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[612,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0153","image_path":"images/combination3d_0153.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0153_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0153_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0153_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0153_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0153_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":153,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2],[1,1,1],[1,2,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[576,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0154","image_path":"images/combination3d_0154.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0154_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0154_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0154_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0154_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0154_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":154,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,1,3],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10}],"canvas_size":[614,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0155","image_path":"images/combination3d_0155.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0155_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0155_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0155_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0155_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0155_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":155,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,3]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,2],[2,1,2],[3,1,2]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[612,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0156","image_path":"images/combination3d_0156.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0156_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0156_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0156_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0156_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0156_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":156,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[612,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0157","image_path":"images/combination3d_0157.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0157_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0157_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0157_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_0157_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0157_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":157,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,3,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0]],[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0]],[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,1],[2,3,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[578,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0158","image_path":"images/combination3d_0158.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0158_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0158_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0158_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_0158_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0158_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":158,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,0,0],[1,0,1],[1,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]]],"total_cube_count":13}],"canvas_size":[600,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0159","image_path":"images/combination3d_0159.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0159_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0159_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0159_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0159_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0159_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":159,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[565,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0160","image_path":"images/combination3d_0160.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0160_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0160_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0160_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0160_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0160_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":160,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[616,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0161","image_path":"images/combination3d_0161.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0161_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0161_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0161_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0161_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0161_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":161,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1],[2,0,2]],[[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,3,3]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,3],[2,0,3],[3,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[1,3,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[556,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0162","image_path":"images/combination3d_0162.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0162_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0162_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0162_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0162_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0162_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":162,"target_cube_count":13,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[1,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11}],"canvas_size":[619,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0163","image_path":"images/combination3d_0163.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0163_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0163_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0163_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0163_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0163_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":163,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,1,1],[0,2,1],[0,2,2],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[562,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0164","image_path":"images/combination3d_0164.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0164_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0164_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0164_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0164_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0164_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":164,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0]],[[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,1,0],[2,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,3],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,2]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[552,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0165","image_path":"images/combination3d_0165.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0165_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0165_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0165_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0165_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0165_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":165,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0],[2,2,0],[2,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,2,3],[0,3,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0],[2,1,0]]],"total_cube_count":13}],"canvas_size":[572,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0166","image_path":"images/combination3d_0166.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0166_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0166_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0166_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0166_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0166_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":166,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[579,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0167","image_path":"images/combination3d_0167.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0167_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0167_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0167_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0167_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0167_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":167,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,1],[3,0,0],[4,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10}],"canvas_size":[564,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0168","image_path":"images/combination3d_0168.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0168_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0168_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0168_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0168_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0168_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":168,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,2,0],[2,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[3,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[582,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0169","image_path":"images/combination3d_0169.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0169_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0169_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0169_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0169_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0169_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":169,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,1],[2,0,2],[2,0,3],[2,1,1],[2,1,3]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[4,0,0],[4,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[1,4,0]]],"total_cube_count":15}],"canvas_size":[594,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0170","image_path":"images/combination3d_0170.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0170_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0170_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0170_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0170_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0170_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":170,"target_cube_count":14,"target_cubes":[[0,3,0],[0,3,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[599,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0171","image_path":"images/combination3d_0171.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0171_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0171_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0171_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_0171_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0171_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":171,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":9}],"canvas_size":[595,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0172","image_path":"images/combination3d_0172.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0172_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0172_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0172_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0172_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0172_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":172,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,1,2],[2,0,2],[2,0,3]]],"total_cube_count":13}],"canvas_size":[591,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0173","image_path":"images/combination3d_0173.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0173_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0173_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0173_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0173_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0173_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":173,"target_cube_count":13,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1],[3,2,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":8}],"canvas_size":[550,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0174","image_path":"images/combination3d_0174.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0174_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0174_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0174_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0174_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0174_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":174,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":8}],"canvas_size":[606,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0175","image_path":"images/combination3d_0175.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0175_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0175_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0175_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0175_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0175_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":175,"target_cube_count":8,"target_cubes":[[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,5,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1],[1,3,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,3]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,3]]],"total_cube_count":14}],"canvas_size":[553,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0176","image_path":"images/combination3d_0176.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0176_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0176_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0176_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0176_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0176_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":176,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,3,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,1],[1,4,1],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,1,2],[1,3,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":12}],"canvas_size":[577,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0177","image_path":"images/combination3d_0177.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0177_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0177_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0177_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0177_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0177_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":177,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,1,0],[1,2,0],[1,2,1],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,1],[1,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]]],"total_cube_count":11}],"canvas_size":[564,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0178","image_path":"images/combination3d_0178.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0178_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0178_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0178_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0178_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0178_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":178,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,4],[0,1,0],[0,1,1],[0,1,2],[1,0,4],[1,1,2],[1,1,3],[1,1,4],[2,1,2],[2,1,3],[2,1,4]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":15}],"canvas_size":[575,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0179","image_path":"images/combination3d_0179.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0179_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0179_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0179_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0179_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0179_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":179,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,3,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1],[1,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,2],[0,1,0],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13}],"canvas_size":[568,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0180","image_path":"images/combination3d_0180.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0180_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0180_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0180_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0180_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_0180_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":180,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[563,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0181","image_path":"images/combination3d_0181.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0181_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0181_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0181_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0181_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0181_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":181,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[607,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0182","image_path":"images/combination3d_0182.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0182_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0182_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0182_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0182_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0182_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":182,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":13}],"canvas_size":[563,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0183","image_path":"images/combination3d_0183.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0183_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0183_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0183_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0183_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0183_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":183,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,2,0]]],"total_cube_count":9}],"canvas_size":[585,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0184","image_path":"images/combination3d_0184.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0184_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0184_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0184_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_0184_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0184_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":184,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9}],"canvas_size":[564,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0185","image_path":"images/combination3d_0185.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0185_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0185_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0185_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0185_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0185_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":185,"target_cube_count":9,"target_cubes":[[0,2,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,1],[1,1,1],[1,1,2],[1,2,2],[2,0,1],[2,1,0],[2,1,1],[3,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12}],"canvas_size":[593,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0186","image_path":"images/combination3d_0186.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0186_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0186_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0186_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0186_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0186_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":186,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11}],"canvas_size":[594,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0187","image_path":"images/combination3d_0187.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0187_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0187_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0187_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0187_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0187_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":187,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[578,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0188","image_path":"images/combination3d_0188.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0188_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0188_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0188_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0188_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0188_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":188,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":13}],"canvas_size":[611,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0189","image_path":"images/combination3d_0189.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0189_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0189_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0189_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0189_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0189_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":189,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,0],[4,0,0],[4,0,1],[4,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,2]],[[0,0,2],[0,1,2],[1,0,2],[1,0,3],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[559,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0190","image_path":"images/combination3d_0190.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0190_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0190_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0190_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0190_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0190_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":190,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,1,1]]],"total_cube_count":12}],"canvas_size":[617,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0191","image_path":"images/combination3d_0191.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0191_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0191_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0191_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_0191_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0191_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":191,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[597,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0192","image_path":"images/combination3d_0192.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0192_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0192_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0192_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0192_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0192_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":192,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3],[1,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3],[1,1,2]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]]],"total_cube_count":14}],"canvas_size":[609,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0193","image_path":"images/combination3d_0193.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0193_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0193_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0193_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0193_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0193_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":193,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[2,0,1],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10}],"canvas_size":[558,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0194","image_path":"images/combination3d_0194.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0194_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0194_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0194_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0194_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0194_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":194,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[600,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0195","image_path":"images/combination3d_0195.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0195_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0195_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0195_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0195_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_0195_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":195,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,0,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,1],[1,1,2],[1,2,1],[1,2,2],[2,0,1],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2],[2,2,3]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0]]],"total_cube_count":13}],"canvas_size":[614,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0196","image_path":"images/combination3d_0196.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0196_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0196_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0196_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0196_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0196_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":196,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[619,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0197","image_path":"images/combination3d_0197.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0197_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0197_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0197_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0197_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_0197_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":197,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,2,1]],[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,2],[1,2,1],[1,2,2],[1,2,3],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[556,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0198","image_path":"images/combination3d_0198.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0198_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0198_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0198_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0198_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0198_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":198,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]]],"total_cube_count":11}],"canvas_size":[594,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0199","image_path":"images/combination3d_0199.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0199_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0199_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0199_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0199_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0199_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":199,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[1,1,1],[2,1,0],[2,1,1],[2,2,1],[3,1,1],[3,2,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]]],"total_cube_count":9}],"canvas_size":[555,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0200","image_path":"images/combination3d_0200.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0200_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0200_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0200_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_0200_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0200_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":200,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[0,2,2],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[558,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0201","image_path":"images/combination3d_0201.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0201_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0201_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0201_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0201_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0201_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":201,"target_cube_count":10,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,2,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[2,3,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]]],"total_cube_count":12}],"canvas_size":[599,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0202","image_path":"images/combination3d_0202.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0202_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0202_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0202_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0202_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0202_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":202,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,2],[2,2,1],[2,3,1],[3,2,1],[4,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,0,0]]],"total_cube_count":15}],"canvas_size":[561,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0203","image_path":"images/combination3d_0203.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0203_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0203_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0203_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0203_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0203_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":203,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[2,0,0]]],"total_cube_count":8}],"canvas_size":[600,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0204","image_path":"images/combination3d_0204.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0204_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0204_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0204_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0204_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0204_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":204,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[3,0,1],[4,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,1,3],[0,1,4],[0,2,1],[0,2,2],[0,3,1],[1,2,0],[1,2,1],[1,2,2],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[605,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0205","image_path":"images/combination3d_0205.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0205_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0205_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0205_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0205_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_0205_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":205,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,2],[1,1,1],[1,1,2],[1,2,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,2,3]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[551,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0206","image_path":"images/combination3d_0206.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0206_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0206_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0206_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0206_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0206_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":206,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":13}],"canvas_size":[614,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0207","image_path":"images/combination3d_0207.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0207_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0207_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0207_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0207_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0207_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":207,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[4,0,0],[4,0,1],[4,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":14}],"canvas_size":[585,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0208","image_path":"images/combination3d_0208.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0208_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0208_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0208_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0208_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0208_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":208,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1]]],"total_cube_count":12}],"canvas_size":[552,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0209","image_path":"images/combination3d_0209.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0209_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0209_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0209_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0209_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0209_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":209,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,0,0],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,3,1],[1,0,3],[1,1,2],[1,1,3],[1,2,3],[1,3,0],[1,3,1],[1,3,2],[1,3,3],[2,1,3],[2,3,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,0,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[599,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0210","image_path":"images/combination3d_0210.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0210_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0210_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0210_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_0210_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0210_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":210,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[595,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0211","image_path":"images/combination3d_0211.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0211_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0211_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0211_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_0211_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0211_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":211,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[600,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0212","image_path":"images/combination3d_0212.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0212_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0212_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0212_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0212_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0212_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":212,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":9}],"canvas_size":[569,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0213","image_path":"images/combination3d_0213.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0213_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0213_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0213_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0213_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0213_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":213,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[616,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0214","image_path":"images/combination3d_0214.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0214_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0214_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0214_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0214_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0214_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":214,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[555,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0215","image_path":"images/combination3d_0215.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0215_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0215_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0215_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0215_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0215_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":215,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[576,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0216","image_path":"images/combination3d_0216.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0216_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0216_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0216_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0216_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_0216_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":216,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,0,1],[4,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,0,1],[4,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9}],"canvas_size":[586,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0217","image_path":"images/combination3d_0217.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0217_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0217_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0217_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0217_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0217_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":217,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,0,1],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":8}],"canvas_size":[588,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0218","image_path":"images/combination3d_0218.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0218_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0218_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0218_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0218_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0218_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":218,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,5,0],[1,3,0],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[593,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0219","image_path":"images/combination3d_0219.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0219_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0219_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0219_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0219_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0219_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":219,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[579,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0220","image_path":"images/combination3d_0220.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0220_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0220_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0220_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0220_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0220_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":220,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,2,0],[1,3,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[581,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0221","image_path":"images/combination3d_0221.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0221_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0221_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0221_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0221_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0221_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":221,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[563,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0222","image_path":"images/combination3d_0222.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0222_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0222_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0222_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0222_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0222_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":222,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[592,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0223","image_path":"images/combination3d_0223.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0223_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0223_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0223_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0223_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0223_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":223,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":9}],"canvas_size":[558,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0224","image_path":"images/combination3d_0224.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0224_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0224_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0224_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0224_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0224_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":224,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,1],[1,2,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13}],"canvas_size":[580,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0225","image_path":"images/combination3d_0225.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0225_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0225_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0225_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0225_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0225_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":225,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,3],[2,0,0],[2,0,3],[2,0,4],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,2,0],[3,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":15}],"canvas_size":[611,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0226","image_path":"images/combination3d_0226.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0226_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0226_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0226_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0226_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_0226_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":226,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[2,1,1],[2,3,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,1],[2,1,2],[3,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1]],[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":14}],"canvas_size":[601,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0227","image_path":"images/combination3d_0227.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0227_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0227_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0227_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0227_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0227_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":227,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":9}],"canvas_size":[578,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0228","image_path":"images/combination3d_0228.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0228_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0228_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0228_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0228_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0228_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":228,"target_cube_count":9,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,2],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[617,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0229","image_path":"images/combination3d_0229.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0229_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0229_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0229_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0229_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0229_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":229,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,1],[2,2,0],[3,1,1],[3,2,0],[3,2,1],[4,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,1],[2,2,0],[3,1,1],[3,2,0],[3,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[1,4,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,2],[0,3,2],[1,2,1],[1,3,1],[1,3,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[570,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0230","image_path":"images/combination3d_0230.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0230_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0230_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0230_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0230_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0230_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":230,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,2,2],[1,0,0],[1,1,1],[1,1,2],[1,2,2],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15}],"canvas_size":[552,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0231","image_path":"images/combination3d_0231.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0231_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0231_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0231_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0231_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0231_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":231,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[2,0,2],[3,0,2],[4,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[585,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0232","image_path":"images/combination3d_0232.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0232_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0232_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0232_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0232_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,6","question_id":"combination3d_0232_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":232,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":9}],"canvas_size":[572,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0233","image_path":"images/combination3d_0233.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0233_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0233_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0233_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0233_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0233_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":233,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1],[3,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,1],[2,1,1]]],"total_cube_count":14}],"canvas_size":[593,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0234","image_path":"images/combination3d_0234.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0234_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0234_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0234_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_0234_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0234_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":234,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[594,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0235","image_path":"images/combination3d_0235.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0235_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0235_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0235_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0235_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0235_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":235,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,1],[1,2,2],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0],[2,1,0],[2,2,0],[2,2,2],[2,3,0],[2,3,1],[2,3,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[597,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0236","image_path":"images/combination3d_0236.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0236_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0236_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0236_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0236_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0236_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":236,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,3,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0]]],"total_cube_count":10}],"canvas_size":[613,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0237","image_path":"images/combination3d_0237.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0237_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0237_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0237_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0237_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_0237_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":237,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,2]]],"total_cube_count":11}],"canvas_size":[597,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0238","image_path":"images/combination3d_0238.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0238_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0238_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0238_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0238_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0238_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":238,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[3,2,1],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,1,0]],[[0,0,2],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,1],[1,1,1],[2,1,1],[2,1,2],[3,0,1],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,1],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[1,3,1],[1,3,2],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":15}],"canvas_size":[565,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0239","image_path":"images/combination3d_0239.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0239_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0239_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0239_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0239_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0239_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":239,"target_cube_count":14,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10}],"canvas_size":[557,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0240","image_path":"images/combination3d_0240.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0240_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0240_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0240_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0240_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0240_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":240,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1]]],"total_cube_count":9}],"canvas_size":[618,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0241","image_path":"images/combination3d_0241.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0241_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0241_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0241_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0241_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0241_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":241,"target_cube_count":8,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[4,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[4,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,2,2]]],"total_cube_count":11}],"canvas_size":[592,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0242","image_path":"images/combination3d_0242.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0242_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0242_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0242_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0242_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0242_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":242,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[2,3,0],[3,2,0],[4,2,0],[4,2,1],[4,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0],[3,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,2],[1,1,1],[2,1,1],[3,0,1],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,3],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[617,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0243","image_path":"images/combination3d_0243.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0243_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0243_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0243_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0243_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0243_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":243,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,2,1],[1,0,2],[1,0,3],[1,1,2],[1,2,0],[1,2,1],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[602,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0244","image_path":"images/combination3d_0244.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0244_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0244_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0244_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0244_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0244_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":244,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11}],"canvas_size":[566,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0245","image_path":"images/combination3d_0245.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0245_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0245_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0245_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0245_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0245_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":245,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[557,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0246","image_path":"images/combination3d_0246.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0246_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0246_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0246_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0246_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0246_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":246,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[2,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":8}],"canvas_size":[608,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0247","image_path":"images/combination3d_0247.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0247_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0247_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0247_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0247_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0247_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":247,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[3,1,0],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,3,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[1,4,0],[1,4,1],[2,0,1],[2,1,1],[2,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,3,0],[0,3,1],[0,4,1],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[2,4,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,4,0],[1,1,0],[1,2,0],[1,3,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,3,0],[0,3,1],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[2,4,0]]],"total_cube_count":14}],"canvas_size":[603,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0248","image_path":"images/combination3d_0248.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0248_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0248_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0248_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0248_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0248_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":248,"target_cube_count":14,"target_cubes":[[0,3,0],[0,3,1],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[2,3,2],[2,3,3],[2,3,4],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[0,1,2],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":14}],"canvas_size":[584,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0249","image_path":"images/combination3d_0249.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0249_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0249_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0249_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0249_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0249_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":249,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[599,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0250","image_path":"images/combination3d_0250.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0250_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0250_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0250_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0250_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0250_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":250,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,1],[1,1,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,1],[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[606,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0251","image_path":"images/combination3d_0251.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0251_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0251_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0251_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0251_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0251_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":251,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[552,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0252","image_path":"images/combination3d_0252.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0252_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0252_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0252_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0252_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0252_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":252,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12}],"canvas_size":[618,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0253","image_path":"images/combination3d_0253.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0253_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0253_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0253_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0253_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0253_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":253,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[0,3,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[597,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0254","image_path":"images/combination3d_0254.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0254_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0254_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0254_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0254_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0254_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":254,"target_cube_count":10,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,3,0],[1,3,1],[2,0,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":13}],"canvas_size":[557,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0255","image_path":"images/combination3d_0255.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0255_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0255_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0255_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0255_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0255_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":255,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,1,0],[2,1,1],[3,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":11}],"canvas_size":[612,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0256","image_path":"images/combination3d_0256.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0256_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0256_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0256_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0256_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0256_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":256,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[590,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0257","image_path":"images/combination3d_0257.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0257_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0257_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0257_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0257_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0257_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":257,"target_cube_count":8,"target_cubes":[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,1],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]]],"total_cube_count":13}],"canvas_size":[559,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0258","image_path":"images/combination3d_0258.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0258_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0258_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0258_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0258_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0258_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":258,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":13}],"canvas_size":[555,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0259","image_path":"images/combination3d_0259.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0259_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0259_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0259_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0259_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_0259_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":259,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2],[1,0,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,2]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11}],"canvas_size":[576,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0260","image_path":"images/combination3d_0260.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0260_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0260_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0260_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0260_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0260_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":260,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[605,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0261","image_path":"images/combination3d_0261.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0261_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0261_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0261_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0261_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_0261_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":261,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,1,1],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[590,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0262","image_path":"images/combination3d_0262.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0262_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0262_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0262_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0262_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0262_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":262,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,1],[1,0,1],[1,2,1],[1,2,2],[1,3,1],[2,0,1],[2,1,1],[2,2,1],[3,0,1],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,1,2],[2,1,3],[3,1,1],[3,1,2],[3,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,0,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,1,1]]],"total_cube_count":12}],"canvas_size":[604,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0263","image_path":"images/combination3d_0263.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0263_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0263_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0263_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0263_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0263_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":263,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,3,0],[1,0,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[587,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0264","image_path":"images/combination3d_0264.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0264_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0264_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0264_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0264_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0264_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":264,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,1],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[3,2,0],[4,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,1],[2,2,1],[2,2,2],[2,2,3],[2,2,4]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,2,0],[3,3,0],[4,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0]]],"total_cube_count":14}],"canvas_size":[600,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0265","image_path":"images/combination3d_0265.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0265_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0265_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0265_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0265_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0265_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":265,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,2,0],[3,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,2,2],[3,2,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,0],[3,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14}],"canvas_size":[558,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0266","image_path":"images/combination3d_0266.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0266_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0266_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0266_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0266_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0266_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":266,"target_cube_count":13,"target_cubes":[[0,3,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,2,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11}],"canvas_size":[575,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0267","image_path":"images/combination3d_0267.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0267_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0267_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0267_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0267_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0267_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":267,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10}],"canvas_size":[618,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0268","image_path":"images/combination3d_0268.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0268_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0268_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0268_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0268_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,6","question_id":"combination3d_0268_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":268,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[555,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0269","image_path":"images/combination3d_0269.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0269_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0269_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0269_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0269_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0269_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":269,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,0,2],[1,1,1],[1,1,2]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,4,0],[1,2,0],[1,3,0],[1,4,0],[2,0,1],[2,1,1],[2,2,1],[2,3,0],[2,3,1],[2,4,0],[2,4,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14}],"canvas_size":[572,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0270","image_path":"images/combination3d_0270.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0270_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0270_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0270_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0270_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0270_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":270,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":10}],"canvas_size":[611,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0271","image_path":"images/combination3d_0271.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0271_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0271_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0271_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0271_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0271_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":271,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[611,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0272","image_path":"images/combination3d_0272.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0272_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0272_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0272_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0272_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0272_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":272,"target_cube_count":8,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13}],"canvas_size":[574,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0273","image_path":"images/combination3d_0273.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0273_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0273_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0273_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_0273_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0273_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":273,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,1,0],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[568,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0274","image_path":"images/combination3d_0274.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0274_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0274_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0274_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0274_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0274_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":274,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[565,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0275","image_path":"images/combination3d_0275.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0275_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0275_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0275_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0275_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0275_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":275,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9}],"canvas_size":[597,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0276","image_path":"images/combination3d_0276.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0276_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0276_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0276_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0276_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0276_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":276,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[561,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0277","image_path":"images/combination3d_0277.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0277_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0277_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0277_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0277_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0277_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":277,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[587,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0278","image_path":"images/combination3d_0278.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0278_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0278_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0278_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0278_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0278_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":278,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,2]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":14}],"canvas_size":[602,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0279","image_path":"images/combination3d_0279.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0279_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0279_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0279_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0279_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0279_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":279,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,1,0],[3,2,0],[3,3,0],[4,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":13}],"canvas_size":[589,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0280","image_path":"images/combination3d_0280.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0280_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0280_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0280_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0280_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0280_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":280,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[0,2,1],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":10}],"canvas_size":[552,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0281","image_path":"images/combination3d_0281.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0281_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0281_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0281_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0281_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0281_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":281,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1],[1,2,1]]],"total_cube_count":13}],"canvas_size":[555,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0282","image_path":"images/combination3d_0282.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0282_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0282_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0282_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0282_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0282_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":282,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[2,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":15}],"canvas_size":[552,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0283","image_path":"images/combination3d_0283.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0283_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0283_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0283_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0283_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0283_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":283,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[554,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0284","image_path":"images/combination3d_0284.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0284_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0284_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0284_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0284_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0284_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":284,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12}],"canvas_size":[586,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0285","image_path":"images/combination3d_0285.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0285_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0285_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0285_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0285_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0285_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":285,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,0,1],[3,0,2],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,2]]],"total_cube_count":10}],"canvas_size":[612,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0286","image_path":"images/combination3d_0286.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0286_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0286_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0286_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0286_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0286_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":286,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10}],"canvas_size":[553,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0287","image_path":"images/combination3d_0287.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0287_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0287_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0287_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0287_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0287_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":287,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":11}],"canvas_size":[586,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0288","image_path":"images/combination3d_0288.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0288_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0288_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0288_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0288_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0288_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":288,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,1,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,3],[0,2,2],[0,2,3],[0,3,2],[0,3,3],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[0,3,4],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]]],"total_cube_count":13}],"canvas_size":[584,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0289","image_path":"images/combination3d_0289.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0289_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0289_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0289_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0289_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0289_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":289,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[619,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0290","image_path":"images/combination3d_0290.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0290_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0290_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0290_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0290_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0290_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":290,"target_cube_count":10,"target_cubes":[[0,0,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,2,1],[2,2,2],[3,2,0],[3,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[610,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0291","image_path":"images/combination3d_0291.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0291_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0291_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0291_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0291_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0291_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":291,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,1,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[568,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0292","image_path":"images/combination3d_0292.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0292_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0292_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0292_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0292_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0292_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":292,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[611,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0293","image_path":"images/combination3d_0293.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0293_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0293_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0293_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0293_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0293_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":293,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":11}],"canvas_size":[572,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0294","image_path":"images/combination3d_0294.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0294_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0294_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0294_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0294_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0294_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":294,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,2],[1,0,3],[2,0,2],[2,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[586,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0295","image_path":"images/combination3d_0295.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0295_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0295_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0295_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0295_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0295_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":295,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":10}],"canvas_size":[559,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0296","image_path":"images/combination3d_0296.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0296_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0296_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0296_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0296_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0296_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":296,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[617,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0297","image_path":"images/combination3d_0297.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0297_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0297_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0297_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0297_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0297_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":297,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,1],[0,1,2],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,0,2],[2,3,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,1],[1,0,1],[1,0,2],[1,1,1],[1,2,0],[1,2,1],[1,3,1],[2,0,1],[2,0,2],[2,0,3],[2,3,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,3],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[576,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0298","image_path":"images/combination3d_0298.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0298_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0298_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0298_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0298_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0298_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":298,"target_cube_count":13,"target_cubes":[[0,3,0],[0,4,0],[0,4,1],[0,4,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,0,2],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2],[1,1,0],[2,0,2],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13}],"canvas_size":[596,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0299","image_path":"images/combination3d_0299.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0299_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0299_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0299_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0299_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0299_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":299,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[595,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0300","image_path":"images/combination3d_0300.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0300_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0300_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0300_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0300_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0300_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":300,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[601,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0301","image_path":"images/combination3d_0301.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0301_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0301_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0301_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0301_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0301_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":301,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1],[3,1,2],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12}],"canvas_size":[618,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0302","image_path":"images/combination3d_0302.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0302_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0302_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0302_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0302_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0302_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":302,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[2,2,1],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,1,2],[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[554,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0303","image_path":"images/combination3d_0303.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0303_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0303_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0303_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0303_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0303_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":303,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2],[1,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":11}],"canvas_size":[567,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0304","image_path":"images/combination3d_0304.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0304_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0304_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0304_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0304_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0304_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":304,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[4,1,0],[4,1,1],[4,1,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[0,2,1],[1,0,3],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,2]]],"total_cube_count":12}],"canvas_size":[573,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0305","image_path":"images/combination3d_0305.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0305_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0305_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0305_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0305_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0305_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":305,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[605,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0306","image_path":"images/combination3d_0306.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0306_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0306_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0306_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0306_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0306_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":306,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0],[4,1,1],[4,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,2],[1,1,2],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,2],[1,0,2],[1,0,3],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,2],[2,0,3]]],"total_cube_count":14}],"canvas_size":[615,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0307","image_path":"images/combination3d_0307.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0307_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0307_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0307_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0307_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0307_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":307,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,3,2]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[573,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0308","image_path":"images/combination3d_0308.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0308_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0308_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0308_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0308_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0308_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":308,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[558,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0309","image_path":"images/combination3d_0309.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0309_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0309_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0309_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0309_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0309_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":309,"target_cube_count":8,"target_cubes":[[0,2,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":9}],"canvas_size":[620,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0310","image_path":"images/combination3d_0310.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0310_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0310_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0310_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_0310_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0310_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":310,"target_cube_count":9,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,0,3],[0,0,4],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[4,0,0],[4,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[583,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0311","image_path":"images/combination3d_0311.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0311_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0311_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0311_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_0311_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0311_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":311,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,0],[0,3,1],[0,4,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[568,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0312","image_path":"images/combination3d_0312.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0312_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0312_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0312_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,5","question_id":"combination3d_0312_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0312_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":312,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[570,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0313","image_path":"images/combination3d_0313.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0313_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0313_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0313_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0313_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0313_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":313,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[575,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0314","image_path":"images/combination3d_0314.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0314_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0314_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0314_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0314_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0314_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":314,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,2,1]]],"total_cube_count":11}],"canvas_size":[602,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0315","image_path":"images/combination3d_0315.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0315_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0315_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0315_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0315_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0315_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":315,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,0,3],[2,0,4]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,3]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1],[2,3,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,3]]],"total_cube_count":14}],"canvas_size":[553,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0316","image_path":"images/combination3d_0316.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0316_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0316_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0316_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0316_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0316_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":316,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[2,2,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,1],[2,1,2],[2,2,1],[2,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[609,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0317","image_path":"images/combination3d_0317.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0317_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0317_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0317_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0317_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0317_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":317,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11}],"canvas_size":[556,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0318","image_path":"images/combination3d_0318.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0318_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0318_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0318_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0318_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0318_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":318,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":8}],"canvas_size":[572,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0319","image_path":"images/combination3d_0319.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0319_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0319_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0319_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0319_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0319_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":319,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,1],[1,0,3],[1,0,4],[1,0,5],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,1],[2,0,3],[2,0,4]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,1],[1,4,0],[1,4,1],[2,1,0],[2,2,0],[2,4,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,2],[2,0,3]]],"total_cube_count":13}],"canvas_size":[607,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0320","image_path":"images/combination3d_0320.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0320_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0320_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0320_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_0320_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0320_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":320,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":9}],"canvas_size":[585,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0321","image_path":"images/combination3d_0321.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0321_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0321_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0321_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0321_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0321_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":321,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,3,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[603,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0322","image_path":"images/combination3d_0322.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0322_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0322_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0322_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0322_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0322_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":322,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,2],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[1,2,2],[1,3,0],[1,3,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,2,1],[0,2,2],[0,3,0],[0,3,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[1,2,1],[2,1,1],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12}],"canvas_size":[564,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0323","image_path":"images/combination3d_0323.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0323_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0323_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0323_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0323_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0323_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":323,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,1],[1,3,0],[1,3,1],[1,3,2],[2,0,1],[2,1,1],[2,2,1],[2,2,2],[2,3,1],[2,3,2],[3,1,1],[4,1,1],[4,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,1],[0,4,1],[1,1,3],[1,2,2],[1,2,3],[1,4,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,1,0],[4,1,0],[4,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[571,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0324","image_path":"images/combination3d_0324.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0324_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0324_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0324_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0324_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_0324_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":324,"target_cube_count":14,"target_cubes":[[0,3,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[2,4,0],[2,4,1],[3,1,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10}],"canvas_size":[620,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0325","image_path":"images/combination3d_0325.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0325_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0325_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0325_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0325_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0325_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":325,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,2],[1,1,0],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[563,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0326","image_path":"images/combination3d_0326.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0326_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0326_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0326_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0326_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0326_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":326,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[557,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0327","image_path":"images/combination3d_0327.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0327_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0327_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0327_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0327_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0327_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":327,"target_cube_count":12,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":10}],"canvas_size":[614,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0328","image_path":"images/combination3d_0328.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0328_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0328_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0328_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0328_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0328_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":328,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[610,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0329","image_path":"images/combination3d_0329.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0329_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0329_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0329_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0329_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0329_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":329,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1]]],"total_cube_count":8}],"canvas_size":[559,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0330","image_path":"images/combination3d_0330.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0330_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0330_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0330_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0330_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0330_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":330,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[591,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0331","image_path":"images/combination3d_0331.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0331_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0331_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0331_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0331_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0331_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":331,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,2,1],[0,3,1],[0,3,2],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12}],"canvas_size":[581,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0332","image_path":"images/combination3d_0332.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0332_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0332_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0332_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0332_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0332_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":332,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,4,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[594,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0333","image_path":"images/combination3d_0333.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0333_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0333_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0333_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0333_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0333_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":333,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[581,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0334","image_path":"images/combination3d_0334.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0334_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0334_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0334_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0334_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0334_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":334,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,0,2],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[2,1,2]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":14}],"canvas_size":[568,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0335","image_path":"images/combination3d_0335.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0335_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0335_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0335_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0335_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0335_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":335,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[2,1,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,3,0],[1,3,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,0,2],[2,1,2],[2,2,2],[3,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[550,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0336","image_path":"images/combination3d_0336.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0336_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0336_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0336_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0336_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0336_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":336,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[3,2,0],[3,3,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[0,3,2],[1,0,4],[1,1,1],[1,1,3],[1,1,4],[2,0,1],[2,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,2],[1,1,0],[2,0,2],[3,0,2],[4,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[0,3,4],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":15}],"canvas_size":[575,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0337","image_path":"images/combination3d_0337.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0337_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0337_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0337_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0337_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0337_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":337,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[2,3,3],[2,3,4],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[0,2,3]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[564,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0338","image_path":"images/combination3d_0338.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0338_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0338_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0338_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0338_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0338_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":338,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,3],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4],[2,1,1],[2,1,2],[2,2,1],[2,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,4,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,4,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,1,3],[1,0,3],[1,1,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,1],[3,1,1],[4,0,1]]],"total_cube_count":14}],"canvas_size":[568,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0339","image_path":"images/combination3d_0339.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0339_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0339_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0339_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0339_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0339_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":339,"target_cube_count":14,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[601,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0340","image_path":"images/combination3d_0340.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0340_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0340_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0340_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_0340_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0340_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":340,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":9}],"canvas_size":[588,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0341","image_path":"images/combination3d_0341.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0341_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0341_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0341_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_0341_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0341_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":341,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[565,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0342","image_path":"images/combination3d_0342.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0342_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0342_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0342_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0342_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0342_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":342,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,1],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[574,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0343","image_path":"images/combination3d_0343.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0343_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0343_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0343_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0343_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0343_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":343,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8}],"canvas_size":[598,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0344","image_path":"images/combination3d_0344.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0344_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0344_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0344_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0344_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0344_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":344,"target_cube_count":8,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,2],[1,2,2]]],"total_cube_count":9}],"canvas_size":[586,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0345","image_path":"images/combination3d_0345.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0345_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0345_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0345_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0345_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0345_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":345,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,1],[1,2,1],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[574,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0346","image_path":"images/combination3d_0346.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0346_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0346_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0346_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0346_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0346_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":346,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[594,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0347","image_path":"images/combination3d_0347.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0347_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0347_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0347_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0347_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0347_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":347,"target_cube_count":11,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[590,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0348","image_path":"images/combination3d_0348.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0348_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0348_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0348_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0348_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0348_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":348,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,3,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,1,1],[0,1,2],[1,0,1],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[602,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0349","image_path":"images/combination3d_0349.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0349_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0349_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0349_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0349_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0349_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":349,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[596,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0350","image_path":"images/combination3d_0350.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0350_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0350_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0350_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0350_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0350_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":350,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,1,1],[2,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,2,0],[1,3,0],[2,3,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":13}],"canvas_size":[594,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0351","image_path":"images/combination3d_0351.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0351_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0351_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0351_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0351_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0351_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":351,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,1]],[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,1,2],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":13}],"canvas_size":[586,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0352","image_path":"images/combination3d_0352.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0352_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0352_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0352_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_0352_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0352_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":352,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[562,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0353","image_path":"images/combination3d_0353.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0353_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0353_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0353_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0353_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0353_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":353,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":8}],"canvas_size":[577,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0354","image_path":"images/combination3d_0354.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0354_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0354_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0354_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0354_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0354_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":354,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,2],[0,1,3],[1,1,2],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[3,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[570,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0355","image_path":"images/combination3d_0355.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0355_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0355_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0355_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0355_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0355_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":355,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,2,1],[4,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":14}],"canvas_size":[555,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0356","image_path":"images/combination3d_0356.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0356_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0356_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0356_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0356_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0356_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":356,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,3,0],[2,3,1],[2,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,1,0],[3,1,1],[3,1,2],[3,1,3]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14}],"canvas_size":[573,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0357","image_path":"images/combination3d_0357.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0357_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0357_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0357_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0357_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0357_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":357,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,1,2],[1,2,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[580,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0358","image_path":"images/combination3d_0358.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0358_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0358_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0358_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0358_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0358_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":358,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,1,0],[3,1,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,2,1],[1,2,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]]],"total_cube_count":12}],"canvas_size":[561,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0359","image_path":"images/combination3d_0359.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0359_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0359_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0359_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0359_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0359_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":359,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[579,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0360","image_path":"images/combination3d_0360.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0360_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0360_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0360_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_0360_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0360_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":360,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,1],[3,0,0],[3,0,1],[3,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":15}],"canvas_size":[566,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0361","image_path":"images/combination3d_0361.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0361_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0361_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0361_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0361_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0361_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":361,"target_cube_count":14,"target_cubes":[[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,0],[2,3,1],[2,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,3],[2,0,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,0,2],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,1],[1,2,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,0,2],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[617,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0362","image_path":"images/combination3d_0362.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0362_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0362_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0362_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0362_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0362_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":362,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1],[2,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":8}],"canvas_size":[571,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0363","image_path":"images/combination3d_0363.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0363_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0363_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0363_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_0363_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0363_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":363,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[2,0,2]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[550,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0364","image_path":"images/combination3d_0364.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0364_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0364_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0364_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0364_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0364_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":364,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[586,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0365","image_path":"images/combination3d_0365.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0365_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0365_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0365_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0365_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0365_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":365,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[1,4,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0],[5,0,0],[5,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2],[2,1,0],[2,1,2]]],"total_cube_count":13}],"canvas_size":[558,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0366","image_path":"images/combination3d_0366.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0366_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0366_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0366_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0366_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0366_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":366,"target_cube_count":13,"target_cubes":[[0,2,0],[0,3,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,0,2],[3,1,0],[3,2,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1],[3,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[554,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0367","image_path":"images/combination3d_0367.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0367_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0367_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0367_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0367_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0367_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":367,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8}],"canvas_size":[611,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0368","image_path":"images/combination3d_0368.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0368_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0368_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0368_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0368_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0368_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":368,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,2,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":10}],"canvas_size":[596,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0369","image_path":"images/combination3d_0369.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0369_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0369_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0369_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0369_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0369_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":369,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0]],[[0,1,1],[1,1,1],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1],[4,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[3,2,2],[4,2,0],[5,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[3,2,2],[4,2,0],[5,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,3],[0,2,3],[0,2,4],[0,2,5],[1,2,2],[1,2,3],[2,1,2],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[565,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0370","image_path":"images/combination3d_0370.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0370_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0370_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0370_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0370_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0370_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":370,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[3,2,2],[4,2,0],[5,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[589,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0371","image_path":"images/combination3d_0371.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0371_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0371_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0371_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0371_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0371_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":371,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,4,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,3]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,0,2],[1,1,1],[1,2,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,4,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[565,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0372","image_path":"images/combination3d_0372.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0372_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0372_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0372_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0372_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0372_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":372,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,4,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,0,1],[2,1,1],[2,1,2],[2,2,0],[2,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,2],[0,3,2],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[554,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0373","image_path":"images/combination3d_0373.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0373_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0373_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0373_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0373_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0373_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":373,"target_cube_count":13,"target_cubes":[[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,3],[2,1,3],[2,2,0],[2,2,2],[2,2,3],[2,2,4]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[2,4,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,1],[2,0,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[2,4,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,2],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2]]],"total_cube_count":13}],"canvas_size":[592,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0374","image_path":"images/combination3d_0374.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0374_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0374_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0374_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0374_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0374_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":374,"target_cube_count":13,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2]]],"total_cube_count":9}],"canvas_size":[579,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0375","image_path":"images/combination3d_0375.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0375_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0375_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0375_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_0375_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0375_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":375,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[3,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,2]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10}],"canvas_size":[601,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0376","image_path":"images/combination3d_0376.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0376_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0376_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0376_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0376_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0376_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":376,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[580,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0377","image_path":"images/combination3d_0377.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0377_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0377_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0377_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0377_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0377_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":377,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,3],[1,1,1],[1,2,2],[1,2,3],[1,3,3]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[4,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":13}],"canvas_size":[552,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0378","image_path":"images/combination3d_0378.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0378_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0378_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0378_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0378_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0378_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":378,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[553,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0379","image_path":"images/combination3d_0379.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0379_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0379_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0379_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0379_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0379_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":379,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,2,1],[0,3,1],[0,3,2],[0,4,1],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,1,2],[1,2,2]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":14}],"canvas_size":[566,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0380","image_path":"images/combination3d_0380.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0380_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0380_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0380_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0380_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0380_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":380,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[3,0,1],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[611,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0381","image_path":"images/combination3d_0381.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0381_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0381_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0381_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0381_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0381_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":381,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":9}],"canvas_size":[557,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0382","image_path":"images/combination3d_0382.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0382_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0382_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0382_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0382_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0382_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":382,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,1],[1,0,2],[1,1,2],[2,1,2],[2,2,2],[3,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[616,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0383","image_path":"images/combination3d_0383.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0383_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0383_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0383_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0383_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0383_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":383,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,1],[0,0,2],[0,1,1],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,1,1],[0,2,1],[1,1,0],[1,1,1],[2,0,1],[2,0,2],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[0,2,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14}],"canvas_size":[599,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0384","image_path":"images/combination3d_0384.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0384_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0384_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0384_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0384_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0384_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":384,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[3,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[558,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0385","image_path":"images/combination3d_0385.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0385_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0385_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0385_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0385_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0385_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":385,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,2,1],[1,3,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[588,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0386","image_path":"images/combination3d_0386.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0386_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0386_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0386_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0386_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0386_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":386,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[606,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0387","image_path":"images/combination3d_0387.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0387_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0387_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0387_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0387_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0387_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":387,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[597,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0388","image_path":"images/combination3d_0388.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0388_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0388_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0388_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0388_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0388_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":388,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,2,1]],[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,3,1],[0,3,2],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":14}],"canvas_size":[595,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0389","image_path":"images/combination3d_0389.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0389_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0389_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0389_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0389_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0389_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":389,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,1],[2,2,0],[2,2,1],[3,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13}],"canvas_size":[561,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0390","image_path":"images/combination3d_0390.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0390_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0390_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0390_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0390_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0390_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":390,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[613,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0391","image_path":"images/combination3d_0391.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0391_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0391_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0391_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0391_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0391_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":391,"target_cube_count":13,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[608,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0392","image_path":"images/combination3d_0392.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0392_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0392_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0392_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0392_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0392_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":392,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[597,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0393","image_path":"images/combination3d_0393.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0393_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0393_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0393_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_0393_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0393_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":393,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0],[3,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[3,0,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,0,1]]],"total_cube_count":10}],"canvas_size":[580,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0394","image_path":"images/combination3d_0394.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0394_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0394_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0394_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0394_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0394_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":394,"target_cube_count":10,"target_cubes":[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[0,2,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[597,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0395","image_path":"images/combination3d_0395.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0395_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0395_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0395_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0395_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0395_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":395,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,1],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[2,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,2],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":13}],"canvas_size":[556,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0396","image_path":"images/combination3d_0396.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0396_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0396_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0396_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0396_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0396_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":396,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[565,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0397","image_path":"images/combination3d_0397.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0397_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0397_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0397_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0397_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0397_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":397,"target_cube_count":11,"target_cubes":[[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9}],"canvas_size":[601,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0398","image_path":"images/combination3d_0398.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0398_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0398_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0398_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0398_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0398_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":398,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0],[3,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0],[3,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,3],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,3],[3,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[554,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0399","image_path":"images/combination3d_0399.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0399_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0399_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0399_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_0399_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0399_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":399,"target_cube_count":13,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,0],[3,2,0],[3,2,1],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[589,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0400","image_path":"images/combination3d_0400.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0400_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0400_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0400_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_0400_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0400_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":400,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[1,4,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[4,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[613,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0401","image_path":"images/combination3d_0401.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0401_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0401_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0401_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0401_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0401_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":401,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,3,0],[3,3,0],[3,4,0],[3,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":13}],"canvas_size":[612,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0402","image_path":"images/combination3d_0402.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0402_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0402_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0402_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0402_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0402_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":402,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[581,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0403","image_path":"images/combination3d_0403.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0403_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0403_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0403_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0403_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0403_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":403,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]]],"total_cube_count":11}],"canvas_size":[561,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0404","image_path":"images/combination3d_0404.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0404_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0404_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0404_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0404_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_0404_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":404,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[555,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0405","image_path":"images/combination3d_0405.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0405_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0405_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0405_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_0405_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0405_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":405,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,4,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[603,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0406","image_path":"images/combination3d_0406.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0406_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0406_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0406_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0406_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0406_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":406,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[4,1,0],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1],[2,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[563,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0407","image_path":"images/combination3d_0407.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0407_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0407_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0407_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0407_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0407_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":407,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,3,1],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[606,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0408","image_path":"images/combination3d_0408.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0408_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0408_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0408_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0408_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0408_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":408,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[616,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0409","image_path":"images/combination3d_0409.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0409_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0409_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0409_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0409_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0409_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":409,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[568,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0410","image_path":"images/combination3d_0410.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0410_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0410_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0410_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0410_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0410_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":410,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[1,3,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[2,1,0],[3,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1]]],"total_cube_count":11}],"canvas_size":[577,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0411","image_path":"images/combination3d_0411.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0411_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0411_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0411_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0411_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0411_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":411,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[1,1,1],[1,2,1],[2,0,1],[2,1,0],[2,1,1],[2,2,1],[2,3,1],[3,2,1],[3,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[3,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[586,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0412","image_path":"images/combination3d_0412.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0412_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0412_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0412_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0412_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0412_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":412,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[609,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0413","image_path":"images/combination3d_0413.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0413_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0413_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0413_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0413_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0413_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":413,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[2,1,0],[2,1,1]]],"total_cube_count":11}],"canvas_size":[604,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0414","image_path":"images/combination3d_0414.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0414_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0414_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0414_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_0414_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0414_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":414,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,1,0],[2,2,1],[3,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[593,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0415","image_path":"images/combination3d_0415.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0415_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0415_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0415_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0415_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0415_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":415,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,1,1],[3,1,2],[3,1,3],[3,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[582,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0416","image_path":"images/combination3d_0416.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0416_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0416_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0416_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_0416_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0416_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":416,"target_cube_count":8,"target_cubes":[[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,0,2],[1,1,1],[1,2,0],[1,2,1],[2,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14}],"canvas_size":[560,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0417","image_path":"images/combination3d_0417.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0417_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0417_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0417_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0417_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0417_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":417,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,1]]],"total_cube_count":8}],"canvas_size":[591,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0418","image_path":"images/combination3d_0418.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0418_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0418_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0418_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0418_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0418_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":418,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[566,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0419","image_path":"images/combination3d_0419.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0419_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0419_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0419_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0419_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0419_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":419,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[1,0,1],[1,1,1],[1,3,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,2],[0,3,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[1,2,2],[2,0,0],[2,0,1],[2,1,2]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[553,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0420","image_path":"images/combination3d_0420.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0420_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0420_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0420_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0420_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0420_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":420,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,1,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[582,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0421","image_path":"images/combination3d_0421.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0421_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0421_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0421_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0421_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0421_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":421,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[599,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0422","image_path":"images/combination3d_0422.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0422_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0422_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0422_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0422_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0422_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":422,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1]]],"total_cube_count":12}],"canvas_size":[591,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0423","image_path":"images/combination3d_0423.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0423_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0423_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0423_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0423_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0423_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":423,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[3,1,0],[4,0,0],[4,1,0],[5,1,0],[5,1,1],[5,1,2],[6,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1]],[[0,1,1],[0,2,1],[0,2,2],[0,3,1],[1,2,1],[2,0,0],[2,0,1],[2,1,1],[2,2,1],[3,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,2],[0,1,1],[0,1,2],[0,1,3],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[3,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1]],[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]]],"total_cube_count":13}],"canvas_size":[609,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0424","image_path":"images/combination3d_0424.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0424_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0424_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0424_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0424_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0424_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":424,"target_cube_count":13,"target_cubes":[[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[603,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0425","image_path":"images/combination3d_0425.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0425_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0425_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0425_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_0425_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0425_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":425,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,0,1],[2,1,1],[3,0,1],[3,1,0],[3,1,1]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,2,1],[0,3,0],[0,3,1],[0,3,2],[0,4,2],[1,0,1],[1,1,1],[1,2,1],[1,3,2],[1,4,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":14}],"canvas_size":[570,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0426","image_path":"images/combination3d_0426.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0426_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0426_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0426_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0426_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0426_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":426,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0]],[[0,0,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,1,1],[2,1,2],[3,1,1],[3,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":15}],"canvas_size":[570,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0427","image_path":"images/combination3d_0427.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0427_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0427_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0427_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0427_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0427_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":427,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[582,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0428","image_path":"images/combination3d_0428.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0428_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0428_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0428_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0428_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0428_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":428,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]],[[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1]]],"total_cube_count":11}],"canvas_size":[565,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0429","image_path":"images/combination3d_0429.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0429_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0429_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0429_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0429_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0429_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":429,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[584,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0430","image_path":"images/combination3d_0430.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0430_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0430_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0430_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0430_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0430_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":430,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8}],"canvas_size":[587,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0431","image_path":"images/combination3d_0431.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0431_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0431_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0431_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0431_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0431_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":431,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,2,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,3,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,2,2],[1,3,1],[1,4,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,3,0]]],"total_cube_count":14}],"canvas_size":[612,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0432","image_path":"images/combination3d_0432.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0432_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0432_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0432_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_0432_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0432_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":432,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[575,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0433","image_path":"images/combination3d_0433.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0433_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0433_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0433_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_0433_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0433_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":433,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":12}],"canvas_size":[596,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0434","image_path":"images/combination3d_0434.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0434_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0434_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0434_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0434_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_0434_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":434,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,1],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[3,2,0],[4,1,0],[4,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[3,2,0],[4,1,0],[4,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[574,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0435","image_path":"images/combination3d_0435.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0435_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0435_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0435_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0435_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0435_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":435,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,3,0],[3,1,0],[3,2,0],[3,3,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,2,1],[2,2,1],[3,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0]]],"total_cube_count":14}],"canvas_size":[598,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0436","image_path":"images/combination3d_0436.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0436_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0436_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0436_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0436_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0436_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":436,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,1,0],[3,1,1],[3,1,2],[3,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8}],"canvas_size":[617,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0437","image_path":"images/combination3d_0437.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0437_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0437_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0437_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0437_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0437_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":437,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[3,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[3,2,0],[4,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,1]]],"total_cube_count":12}],"canvas_size":[576,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0438","image_path":"images/combination3d_0438.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0438_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0438_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0438_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0438_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0438_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":438,"target_cube_count":12,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,2,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[3,1,1]]],"total_cube_count":10}],"canvas_size":[601,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0439","image_path":"images/combination3d_0439.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0439_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0439_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0439_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0439_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0439_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":439,"target_cube_count":10,"target_cubes":[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[565,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0440","image_path":"images/combination3d_0440.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0440_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0440_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0440_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0440_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0440_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":440,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,1],[3,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,3,0],[0,3,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[2,1,0],[2,1,1]]],"total_cube_count":14}],"canvas_size":[572,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0441","image_path":"images/combination3d_0441.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0441_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0441_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0441_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0441_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0441_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":441,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":11}],"canvas_size":[596,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0442","image_path":"images/combination3d_0442.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0442_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0442_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0442_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0442_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0442_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":442,"target_cube_count":11,"target_cubes":[[0,3,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0],[3,3,1],[3,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[566,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0443","image_path":"images/combination3d_0443.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0443_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0443_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0443_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0443_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0443_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":443,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[589,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0444","image_path":"images/combination3d_0444.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0444_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0444_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0444_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0444_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0444_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":444,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[620,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0445","image_path":"images/combination3d_0445.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0445_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0445_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0445_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0445_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_0445_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":445,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,2,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,2,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,2,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,2,3]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[611,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0446","image_path":"images/combination3d_0446.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0446_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0446_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0446_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_0446_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0446_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":446,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,3]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,2]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12}],"canvas_size":[602,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0447","image_path":"images/combination3d_0447.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0447_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0447_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0447_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0447_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0447_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":447,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[585,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0448","image_path":"images/combination3d_0448.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0448_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0448_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0448_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0448_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0448_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":448,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[1,2,1],[2,1,1],[2,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,1],[2,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1]]],"total_cube_count":9}],"canvas_size":[574,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0449","image_path":"images/combination3d_0449.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0449_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0449_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0449_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0449_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_0449_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":449,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[4,1,0],[4,2,0],[4,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,4],[0,2,4],[1,2,2],[1,2,3],[1,2,4],[2,0,2],[2,1,2],[2,1,3],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[4,0,0],[4,1,0],[4,2,0],[4,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":15}],"canvas_size":[562,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0450","image_path":"images/combination3d_0450.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0450_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0450_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0450_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0450_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0450_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":450,"target_cube_count":14,"target_cubes":[[0,0,0],[1,0,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[4,1,0],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[555,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0451","image_path":"images/combination3d_0451.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0451_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0451_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0451_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0451_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0451_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":451,"target_cube_count":9,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[2,1,2],[2,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[593,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0452","image_path":"images/combination3d_0452.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0452_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0452_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0452_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0452_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0452_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":452,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[1,0,1],[1,0,2],[2,0,1],[3,0,0],[3,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[580,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0453","image_path":"images/combination3d_0453.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0453_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0453_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0453_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0453_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0453_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":453,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,2],[2,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[2,1,1]]],"total_cube_count":13}],"canvas_size":[588,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0454","image_path":"images/combination3d_0454.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0454_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0454_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0454_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0454_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0454_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":454,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2]],[[0,0,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[3,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[3,1,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15}],"canvas_size":[553,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0455","image_path":"images/combination3d_0455.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0455_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0455_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0455_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0455_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0455_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":455,"target_cube_count":14,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,2,0],[3,2,1],[3,3,0],[3,3,1],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[607,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0456","image_path":"images/combination3d_0456.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0456_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0456_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0456_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0456_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0456_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":456,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,0,1],[1,1,2],[1,2,1],[2,1,2],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[573,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0457","image_path":"images/combination3d_0457.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0457_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0457_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0457_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0457_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0457_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":457,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,1,2],[1,2,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[2,1,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[559,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0458","image_path":"images/combination3d_0458.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0458_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0458_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0458_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_0458_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0458_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":458,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,2,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[569,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0459","image_path":"images/combination3d_0459.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0459_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0459_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0459_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0459_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_0459_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":459,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,0,1],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,3],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2],[1,3,3]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,1]],[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[2,1,1],[2,1,2],[3,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0],[1,4,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14}],"canvas_size":[588,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0460","image_path":"images/combination3d_0460.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0460_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0460_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0460_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_0460_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0460_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":460,"target_cube_count":14,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[590,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0461","image_path":"images/combination3d_0461.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0461_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0461_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0461_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0461_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0461_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":461,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,1,0]]],"total_cube_count":11}],"canvas_size":[559,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0462","image_path":"images/combination3d_0462.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0462_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0462_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0462_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0462_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0462_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":462,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,0,3],[2,1,2],[3,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[576,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0463","image_path":"images/combination3d_0463.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0463_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0463_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0463_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0463_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0463_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":463,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1],[4,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[0,3,2],[0,4,1],[1,2,0],[1,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,1,1],[3,2,0],[4,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[584,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0464","image_path":"images/combination3d_0464.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0464_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0464_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0464_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0464_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0464_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":464,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[4,1,0],[4,1,1],[4,2,0],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[574,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0465","image_path":"images/combination3d_0465.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0465_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0465_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0465_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0465_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,5","question_id":"combination3d_0465_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":465,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[556,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0466","image_path":"images/combination3d_0466.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0466_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0466_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0466_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_0466_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0466_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":466,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[582,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0467","image_path":"images/combination3d_0467.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0467_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0467_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0467_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0467_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0467_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":467,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":8}],"canvas_size":[576,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0468","image_path":"images/combination3d_0468.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0468_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0468_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0468_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0468_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0468_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":468,"target_cube_count":8,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[583,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0469","image_path":"images/combination3d_0469.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0469_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0469_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0469_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0469_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0469_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":469,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,1,1],[1,2,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[555,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0470","image_path":"images/combination3d_0470.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0470_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0470_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0470_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0470_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0470_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":470,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":10}],"canvas_size":[558,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0471","image_path":"images/combination3d_0471.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0471_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0471_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0471_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0471_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0471_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":471,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0],[3,2,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[569,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0472","image_path":"images/combination3d_0472.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0472_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0472_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0472_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0472_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_0472_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":472,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[593,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0473","image_path":"images/combination3d_0473.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0473_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0473_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0473_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0473_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0473_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":473,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,2],[1,1,1],[1,2,1],[1,3,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":11}],"canvas_size":[558,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0474","image_path":"images/combination3d_0474.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0474_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0474_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0474_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0474_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0474_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":474,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,4,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1],[2,0,1]]],"total_cube_count":14}],"canvas_size":[558,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0475","image_path":"images/combination3d_0475.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0475_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0475_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0475_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0475_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0475_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":475,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,3,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[613,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0476","image_path":"images/combination3d_0476.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0476_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0476_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0476_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0476_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0476_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":476,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[603,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0477","image_path":"images/combination3d_0477.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0477_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0477_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0477_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0477_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0477_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":477,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0],[3,0,1],[3,0,2],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]]],"total_cube_count":9}],"canvas_size":[591,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0478","image_path":"images/combination3d_0478.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0478_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0478_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0478_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_0478_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0478_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":478,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,2],[0,3,2],[1,0,0],[1,1,1],[1,3,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[3,2,0],[3,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[3,2,0],[3,2,1],[4,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[603,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0479","image_path":"images/combination3d_0479.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0479_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0479_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0479_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0479_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0479_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":479,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,2,0],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,2,0],[4,1,0],[4,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[3,1,0],[3,1,1],[4,1,0],[4,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[4,0,0],[4,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[600,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0480","image_path":"images/combination3d_0480.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0480_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0480_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0480_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0480_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0480_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":480,"target_cube_count":14,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[610,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0481","image_path":"images/combination3d_0481.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0481_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0481_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0481_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0481_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0481_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":481,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[616,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0482","image_path":"images/combination3d_0482.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0482_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0482_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0482_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0482_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0482_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":482,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[2,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,0,2],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[617,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0483","image_path":"images/combination3d_0483.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0483_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0483_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0483_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0483_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_0483_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":483,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[1,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10}],"canvas_size":[570,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0484","image_path":"images/combination3d_0484.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0484_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0484_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0484_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0484_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0484_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":484,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,0],[1,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,1],[1,1,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,2],[0,3,0],[0,3,1],[0,3,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,3],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0]]],"total_cube_count":15}],"canvas_size":[567,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0485","image_path":"images/combination3d_0485.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0485_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0485_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0485_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_0485_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0485_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":485,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[0,4,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,1,1],[2,0,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12}],"canvas_size":[572,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0486","image_path":"images/combination3d_0486.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0486_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0486_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0486_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0486_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0486_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":486,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,3,1],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,0,1],[3,1,0],[4,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14}],"canvas_size":[597,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0487","image_path":"images/combination3d_0487.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0487_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0487_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0487_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0487_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0487_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":487,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,0,3],[1,1,2],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,1]],[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[564,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0488","image_path":"images/combination3d_0488.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0488_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0488_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0488_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0488_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0488_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":488,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[2,0,1],[2,1,0],[2,1,1],[3,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[572,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0489","image_path":"images/combination3d_0489.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0489_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0489_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0489_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0489_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0489_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":489,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,1,2]]],"total_cube_count":11}],"canvas_size":[610,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0490","image_path":"images/combination3d_0490.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0490_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0490_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0490_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0490_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0490_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":490,"target_cube_count":11,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,2],[1,1,1],[1,1,2],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[613,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0491","image_path":"images/combination3d_0491.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0491_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0491_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0491_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0491_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0491_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":491,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,1,2],[4,1,0],[4,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,0,1],[3,0,2],[4,0,0],[4,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[563,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0492","image_path":"images/combination3d_0492.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0492_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0492_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0492_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0492_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0492_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":492,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,0,1],[3,0,2],[4,0,0],[4,0,1],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1],[3,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,2,2],[2,1,1],[2,2,1],[2,3,0],[2,3,1],[2,3,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14}],"canvas_size":[582,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0493","image_path":"images/combination3d_0493.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0493_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0493_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0493_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0493_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0493_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":493,"target_cube_count":14,"target_cubes":[[0,4,0],[0,4,1],[0,4,2],[0,4,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[569,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0494","image_path":"images/combination3d_0494.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0494_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0494_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0494_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0494_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0494_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":494,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,1],[4,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,2],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12}],"canvas_size":[570,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0495","image_path":"images/combination3d_0495.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0495_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0495_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0495_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,5","question_id":"combination3d_0495_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0495_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":495,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[607,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0496","image_path":"images/combination3d_0496.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0496_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0496_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0496_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0496_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0496_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":496,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,1,1],[1,1,0],[1,1,1],[2,1,1],[2,1,2],[3,0,1],[3,1,0],[3,1,1],[3,1,2]]],"total_cube_count":13}],"canvas_size":[583,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0497","image_path":"images/combination3d_0497.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0497_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0497_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0497_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0497_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0497_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":497,"target_cube_count":13,"target_cubes":[[0,0,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,0,1],[2,1,1],[2,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,4,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,3,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":13}],"canvas_size":[611,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0498","image_path":"images/combination3d_0498.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0498_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0498_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0498_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0498_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0498_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":498,"target_cube_count":12,"target_cubes":[[0,3,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[3,3,0],[3,3,1],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1],[3,2,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,3],[1,0,3],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[564,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0499","image_path":"images/combination3d_0499.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0499_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0499_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0499_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0499_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0499_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":499,"target_cube_count":14,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,0,2],[3,1,0],[3,2,0],[3,2,1],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,2],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[609,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0500","image_path":"images/combination3d_0500.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0500_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0500_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0500_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0500_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0500_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":500,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,2,1],[1,3,1],[1,3,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[1,2,2],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[586,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0501","image_path":"images/combination3d_0501.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0501_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0501_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0501_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0501_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0501_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":501,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0],[4,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[0,4,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,2]]],"total_cube_count":9}],"canvas_size":[614,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0502","image_path":"images/combination3d_0502.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0502_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0502_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0502_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0502_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_0502_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":502,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0],[4,2,0],[5,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":10}],"canvas_size":[571,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0503","image_path":"images/combination3d_0503.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0503_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0503_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0503_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0503_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0503_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":503,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[0,5,0],[1,2,0],[1,3,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":12}],"canvas_size":[609,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0504","image_path":"images/combination3d_0504.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0504_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0504_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0504_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0504_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0504_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":504,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,1,1],[1,0,1],[1,0,2],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15}],"canvas_size":[569,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0505","image_path":"images/combination3d_0505.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0505_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0505_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0505_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0505_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0505_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":505,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,2]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[612,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0506","image_path":"images/combination3d_0506.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0506_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0506_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0506_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0506_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0506_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":506,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[3,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[611,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0507","image_path":"images/combination3d_0507.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0507_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0507_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0507_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0507_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0507_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":507,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,3,0],[2,3,1],[2,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[3,0,1],[3,1,1],[3,2,0],[3,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1],[3,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,1,2]]],"total_cube_count":13}],"canvas_size":[619,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0508","image_path":"images/combination3d_0508.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0508_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0508_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0508_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0508_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0508_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":508,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,2],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":9}],"canvas_size":[603,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0509","image_path":"images/combination3d_0509.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0509_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0509_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0509_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_0509_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0509_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":509,"target_cube_count":9,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,1,0]],[[0,1,2],[1,1,1],[1,1,2],[1,1,3],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":15}],"canvas_size":[620,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0510","image_path":"images/combination3d_0510.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0510_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0510_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0510_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0510_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0510_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":510,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[563,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0511","image_path":"images/combination3d_0511.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0511_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0511_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0511_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0511_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0511_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":511,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,2],[1,1,0],[2,0,2],[2,1,0],[2,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,2],[1,1,0],[2,0,2],[2,1,0]]],"total_cube_count":11}],"canvas_size":[552,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0512","image_path":"images/combination3d_0512.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0512_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0512_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0512_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0512_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0512_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":512,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,1,1],[3,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1]]],"total_cube_count":9}],"canvas_size":[552,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0513","image_path":"images/combination3d_0513.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0513_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0513_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0513_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0513_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0513_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":513,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[0,3,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[0,3,1],[1,0,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,1],[0,2,2],[1,0,3],[1,1,2],[2,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[595,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0514","image_path":"images/combination3d_0514.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0514_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0514_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0514_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0514_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0514_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":514,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10}],"canvas_size":[571,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0515","image_path":"images/combination3d_0515.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0515_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0515_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0515_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0515_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,6","question_id":"combination3d_0515_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":515,"target_cube_count":10,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,2,0],[3,2,0],[4,0,1],[4,1,0],[4,1,1],[4,1,2],[4,2,0],[4,2,1],[4,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,3,2],[0,4,1],[0,4,2],[1,4,1],[1,4,2],[2,4,1],[2,4,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,2,0],[3,2,0],[4,1,0],[4,1,1],[4,1,2],[4,2,0],[4,2,1],[4,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[580,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0516","image_path":"images/combination3d_0516.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0516_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0516_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0516_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0516_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0516_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":516,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0],[4,1,1],[4,1,2],[4,2,0],[4,2,1],[4,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,0,0],[1,0,1],[1,3,1],[2,3,1],[3,3,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,2],[2,0,0],[2,0,1]]],"total_cube_count":13}],"canvas_size":[605,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0517","image_path":"images/combination3d_0517.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0517_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0517_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0517_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0517_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0517_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":517,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[1,4,2],[1,4,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,0,0],[1,1,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[597,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0518","image_path":"images/combination3d_0518.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0518_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0518_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0518_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0518_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0518_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":518,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,1,0],[0,1,1],[0,2,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":10}],"canvas_size":[606,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0519","image_path":"images/combination3d_0519.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0519_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0519_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0519_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0519_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0519_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":519,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1]],[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,1,2],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,2],[0,0,3],[1,0,2],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4],[2,2,4],[3,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]],[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[551,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0520","image_path":"images/combination3d_0520.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0520_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0520_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0520_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0520_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0520_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":520,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[562,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0521","image_path":"images/combination3d_0521.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0521_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0521_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0521_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0521_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0521_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":521,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[559,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0522","image_path":"images/combination3d_0522.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0522_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0522_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0522_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0522_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0522_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":522,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[586,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0523","image_path":"images/combination3d_0523.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0523_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0523_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0523_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0523_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0523_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":523,"target_cube_count":12,"target_cubes":[[0,2,0],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,0],[2,0,2],[2,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[578,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0524","image_path":"images/combination3d_0524.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0524_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0524_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0524_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0524_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0524_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":524,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[619,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0525","image_path":"images/combination3d_0525.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0525_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0525_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0525_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0525_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0525_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":525,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[569,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0526","image_path":"images/combination3d_0526.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0526_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0526_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0526_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0526_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0526_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":526,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[3,0,0],[3,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":10}],"canvas_size":[605,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0527","image_path":"images/combination3d_0527.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0527_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0527_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0527_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0527_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0527_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":527,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[557,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0528","image_path":"images/combination3d_0528.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0528_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0528_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0528_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0528_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0528_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":528,"target_cube_count":14,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,1],[0,1,2],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,2,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,1,0],[2,2,0],[2,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,1],[0,3,2],[1,1,2]]],"total_cube_count":14}],"canvas_size":[569,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0529","image_path":"images/combination3d_0529.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0529_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0529_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0529_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0529_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0529_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":529,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1]],[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,2,0],[3,2,0],[3,2,1]]],"total_cube_count":14}],"canvas_size":[592,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0530","image_path":"images/combination3d_0530.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0530_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0530_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0530_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0530_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0530_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":530,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[3,2,0],[4,2,0],[5,2,0],[5,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[566,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0531","image_path":"images/combination3d_0531.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0531_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0531_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0531_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0531_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0531_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":531,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[576,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0532","image_path":"images/combination3d_0532.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0532_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0532_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0532_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0532_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0532_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":532,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[598,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0533","image_path":"images/combination3d_0533.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0533_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0533_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0533_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0533_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0533_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":533,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,2,1],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[604,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0534","image_path":"images/combination3d_0534.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0534_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0534_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0534_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0534_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0534_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":534,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[0,3,2]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[568,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0535","image_path":"images/combination3d_0535.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0535_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0535_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0535_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0535_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0535_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":535,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,0,1],[2,1,1],[3,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,2],[2,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[574,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0536","image_path":"images/combination3d_0536.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0536_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0536_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0536_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0536_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0536_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":536,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":10}],"canvas_size":[606,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0537","image_path":"images/combination3d_0537.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0537_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0537_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0537_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0537_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0537_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":537,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":8}],"canvas_size":[584,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0538","image_path":"images/combination3d_0538.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0538_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0538_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0538_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0538_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0538_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":538,"target_cube_count":8,"target_cubes":[[0,2,0],[0,3,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":14}],"canvas_size":[587,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0539","image_path":"images/combination3d_0539.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0539_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0539_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0539_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0539_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0539_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":539,"target_cube_count":14,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[597,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0540","image_path":"images/combination3d_0540.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0540_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0540_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0540_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0540_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0540_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":540,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":11}],"canvas_size":[595,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0541","image_path":"images/combination3d_0541.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0541_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0541_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0541_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0541_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0541_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":541,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,1]]],"total_cube_count":9}],"canvas_size":[611,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0542","image_path":"images/combination3d_0542.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0542_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0542_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0542_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0542_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0542_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":542,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,3,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11}],"canvas_size":[566,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0543","image_path":"images/combination3d_0543.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0543_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0543_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0543_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0543_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0543_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":543,"target_cube_count":11,"target_cubes":[[0,0,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,1,0],[2,2,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[585,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0544","image_path":"images/combination3d_0544.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0544_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0544_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0544_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0544_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0544_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":544,"target_cube_count":10,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,3,0],[0,3,1],[1,0,2],[1,1,2],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[1,3,2],[2,2,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,3,2],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[577,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0545","image_path":"images/combination3d_0545.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0545_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0545_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0545_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0545_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0545_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":545,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[3,2,0],[3,3,0],[3,3,1],[4,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[551,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0546","image_path":"images/combination3d_0546.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0546_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0546_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0546_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0546_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0546_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":546,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":13}],"canvas_size":[555,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0547","image_path":"images/combination3d_0547.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0547_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0547_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0547_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0547_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0547_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":547,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,4,0],[1,4,1],[1,4,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[554,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0548","image_path":"images/combination3d_0548.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0548_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0548_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0548_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_0548_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0548_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":548,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[575,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0549","image_path":"images/combination3d_0549.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0549_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0549_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0549_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0549_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_0549_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":549,"target_cube_count":9,"target_cubes":[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[610,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0550","image_path":"images/combination3d_0550.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0550_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0550_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0550_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0550_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_0550_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":550,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,3,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,2,0],[1,3,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,2,0],[1,3,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[615,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0551","image_path":"images/combination3d_0551.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0551_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0551_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0551_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0551_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0551_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":551,"target_cube_count":13,"target_cubes":[[0,4,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[1,4,2],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[552,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0552","image_path":"images/combination3d_0552.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0552_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0552_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0552_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0552_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0552_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":552,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,1],[2,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[610,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0553","image_path":"images/combination3d_0553.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0553_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0553_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0553_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0553_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0553_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":553,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,1]]],"total_cube_count":9}],"canvas_size":[615,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0554","image_path":"images/combination3d_0554.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0554_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0554_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0554_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0554_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0554_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":554,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[574,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0555","image_path":"images/combination3d_0555.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0555_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0555_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0555_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0555_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0555_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":555,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[0,2,0],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":13}],"canvas_size":[610,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0556","image_path":"images/combination3d_0556.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0556_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0556_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0556_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0556_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_0556_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":556,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[553,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0557","image_path":"images/combination3d_0557.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0557_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0557_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0557_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_0557_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0557_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":557,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,1],[2,1,1],[2,1,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,1],[2,1,1]]],"total_cube_count":10}],"canvas_size":[599,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0558","image_path":"images/combination3d_0558.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0558_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0558_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0558_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0558_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0558_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":558,"target_cube_count":10,"target_cubes":[[0,2,0],[1,2,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[3,3,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,3],[1,0,1],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2],[2,0,3]]],"total_cube_count":11}],"canvas_size":[551,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0559","image_path":"images/combination3d_0559.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0559_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0559_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0559_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0559_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0559_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":559,"target_cube_count":11,"target_cubes":[[0,2,0],[0,3,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,3],[1,0,2],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,2],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[555,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0560","image_path":"images/combination3d_0560.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0560_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0560_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0560_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0560_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0560_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":560,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[617,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0561","image_path":"images/combination3d_0561.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0561_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0561_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0561_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0561_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0561_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":561,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0],[1,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,2],[2,2,2],[3,2,2]]],"total_cube_count":14}],"canvas_size":[597,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0562","image_path":"images/combination3d_0562.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0562_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0562_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0562_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0562_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_0562_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":562,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[2,2,1],[2,3,1],[3,1,1],[3,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[2,1,2],[2,1,3],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[616,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0563","image_path":"images/combination3d_0563.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0563_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0563_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0563_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0563_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_0563_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":563,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,1,0],[3,2,0],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2],[1,2,3]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1],[3,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[587,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0564","image_path":"images/combination3d_0564.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0564_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0564_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0564_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0564_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0564_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":564,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0],[3,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11}],"canvas_size":[610,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0565","image_path":"images/combination3d_0565.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0565_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0565_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0565_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0565_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0565_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":565,"target_cube_count":10,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[1,3,2],[1,3,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14}],"canvas_size":[612,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0566","image_path":"images/combination3d_0566.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0566_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0566_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0566_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0566_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0566_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":566,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[0,3,4],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":12}],"canvas_size":[568,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0567","image_path":"images/combination3d_0567.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0567_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0567_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0567_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0567_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0567_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":567,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[563,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0568","image_path":"images/combination3d_0568.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0568_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0568_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0568_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0568_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0568_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":568,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11}],"canvas_size":[618,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0569","image_path":"images/combination3d_0569.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0569_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0569_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0569_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0569_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0569_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":569,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":9}],"canvas_size":[559,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0570","image_path":"images/combination3d_0570.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0570_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0570_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0570_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0570_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0570_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":570,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2],[4,0,1],[5,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[2,0,1],[2,0,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,2],[2,1,1],[2,1,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":15}],"canvas_size":[569,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0571","image_path":"images/combination3d_0571.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0571_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0571_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0571_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_0571_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0571_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":571,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0],[3,0,1],[3,0,2],[3,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,1],[1,0,2],[1,0,3],[1,0,4]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":10}],"canvas_size":[577,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0572","image_path":"images/combination3d_0572.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0572_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0572_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0572_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0572_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0572_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":572,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[583,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0573","image_path":"images/combination3d_0573.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0573_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0573_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0573_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0573_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_0573_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":573,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,2],[2,1,2]]],"total_cube_count":12}],"canvas_size":[589,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0574","image_path":"images/combination3d_0574.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0574_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0574_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0574_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0574_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0574_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":574,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[1,3,1],[2,0,1],[2,1,1],[3,0,1],[3,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[589,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0575","image_path":"images/combination3d_0575.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0575_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0575_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0575_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_0575_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0575_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":575,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[612,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0576","image_path":"images/combination3d_0576.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0576_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0576_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0576_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0576_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0576_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":576,"target_cube_count":8,"target_cubes":[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,3],[2,1,2],[2,1,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,1],[0,0,2],[0,1,2],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,2],[0,2,2],[0,3,2],[1,0,0],[1,0,1],[1,2,2],[2,2,2],[2,2,3]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,3],[2,1,2],[2,1,3],[3,1,3]]],"total_cube_count":14}],"canvas_size":[600,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0577","image_path":"images/combination3d_0577.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0577_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0577_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0577_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0577_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0577_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":577,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[3,1,0],[3,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[3,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[587,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0578","image_path":"images/combination3d_0578.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0578_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0578_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0578_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0578_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0578_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":578,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[590,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0579","image_path":"images/combination3d_0579.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0579_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0579_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0579_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0579_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0579_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":579,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10}],"canvas_size":[617,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0580","image_path":"images/combination3d_0580.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0580_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0580_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0580_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0580_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_0580_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":580,"target_cube_count":10,"target_cubes":[[0,4,0],[1,3,0],[1,4,0],[2,2,0],[2,3,0],[2,4,0],[3,0,0],[3,1,0],[3,2,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[550,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0581","image_path":"images/combination3d_0581.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0581_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0581_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0581_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0581_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0581_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":581,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9}],"canvas_size":[576,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0582","image_path":"images/combination3d_0582.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0582_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0582_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0582_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0582_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0582_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":582,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[618,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0583","image_path":"images/combination3d_0583.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0583_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0583_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0583_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0583_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0583_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":583,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8}],"canvas_size":[582,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0584","image_path":"images/combination3d_0584.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0584_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0584_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0584_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0584_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0584_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":584,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,2],[2,0,2],[2,1,2]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[557,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0585","image_path":"images/combination3d_0585.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0585_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0585_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0585_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0585_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0585_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":585,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,2],[0,2,4]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,0,1],[3,1,1]]],"total_cube_count":14}],"canvas_size":[585,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0586","image_path":"images/combination3d_0586.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0586_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0586_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0586_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0586_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0586_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":586,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":13}],"canvas_size":[591,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0587","image_path":"images/combination3d_0587.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0587_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0587_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0587_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0587_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0587_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":587,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,3,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":9}],"canvas_size":[601,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0588","image_path":"images/combination3d_0588.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0588_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0588_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0588_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_0588_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0588_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":588,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]],[[0,3,0],[1,3,0],[1,3,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1]]],"total_cube_count":13}],"canvas_size":[565,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0589","image_path":"images/combination3d_0589.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0589_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0589_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0589_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0589_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0589_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":589,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,1,1],[3,1,2],[3,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[553,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0590","image_path":"images/combination3d_0590.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0590_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0590_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0590_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0590_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0590_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":590,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0],[4,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[2,0,5]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,0,3],[2,0,4]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":12}],"canvas_size":[620,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0591","image_path":"images/combination3d_0591.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0591_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0591_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0591_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,5","question_id":"combination3d_0591_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0591_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":591,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12}],"canvas_size":[559,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0592","image_path":"images/combination3d_0592.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0592_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0592_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0592_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0592_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0592_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":592,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,2,0],[1,3,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,0,1],[3,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,3,0],[1,4,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[590,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0593","image_path":"images/combination3d_0593.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0593_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0593_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0593_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0593_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0593_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":593,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,2],[0,1,3],[0,2,3],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,2],[1,0,2],[1,1,1],[1,2,2],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[566,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0594","image_path":"images/combination3d_0594.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0594_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0594_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0594_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0594_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0594_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":594,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,3],[0,1,4],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14}],"canvas_size":[595,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0595","image_path":"images/combination3d_0595.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0595_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0595_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0595_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0595_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0595_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":595,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[601,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0596","image_path":"images/combination3d_0596.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0596_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0596_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0596_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0596_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0596_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":596,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,5,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[562,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0597","image_path":"images/combination3d_0597.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0597_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0597_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0597_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0597_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0597_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":597,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[1,0,0],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,3,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[562,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0598","image_path":"images/combination3d_0598.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0598_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0598_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0598_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0598_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0598_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":598,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":8}],"canvas_size":[554,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0599","image_path":"images/combination3d_0599.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0599_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0599_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0599_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_0599_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0599_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":599,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,1,1],[3,1,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":13}],"canvas_size":[583,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0600","image_path":"images/combination3d_0600.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0600_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0600_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0600_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0600_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0600_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":600,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[2,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12}],"canvas_size":[574,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0601","image_path":"images/combination3d_0601.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0601_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0601_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0601_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0601_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0601_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":601,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,0,1],[3,0,1],[3,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2],[0,1,3],[1,0,0],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[601,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0602","image_path":"images/combination3d_0602.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0602_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0602_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0602_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0602_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0602_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":602,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,0,1],[3,1,0],[3,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[1,4,1],[2,3,1]]],"total_cube_count":12}],"canvas_size":[571,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0603","image_path":"images/combination3d_0603.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0603_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0603_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0603_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0603_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0603_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":603,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[4,0,0],[4,0,1],[4,0,2],[5,0,0],[5,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[3,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[558,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0604","image_path":"images/combination3d_0604.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0604_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0604_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0604_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0604_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0604_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":604,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[1,5,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[1,2,2]]],"total_cube_count":13}],"canvas_size":[572,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0605","image_path":"images/combination3d_0605.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0605_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0605_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0605_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0605_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0605_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":605,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,2,0],[0,2,1],[1,2,1],[1,2,2],[2,2,1],[3,0,1],[3,1,1],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0]]],"total_cube_count":13}],"canvas_size":[557,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0606","image_path":"images/combination3d_0606.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0606_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0606_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0606_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0606_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0606_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":606,"target_cube_count":13,"target_cubes":[[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0]]],"total_cube_count":8}],"canvas_size":[560,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0607","image_path":"images/combination3d_0607.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0607_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0607_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0607_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0607_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0607_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":607,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9}],"canvas_size":[566,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0608","image_path":"images/combination3d_0608.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0608_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0608_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0608_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0608_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_0608_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":608,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[589,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0609","image_path":"images/combination3d_0609.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0609_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0609_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0609_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_0609_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0609_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":609,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,1,1],[2,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1]]],"total_cube_count":11}],"canvas_size":[606,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0610","image_path":"images/combination3d_0610.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0610_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0610_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0610_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0610_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0610_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":610,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,1,0],[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,2,0],[2,0,0],[2,2,0],[3,2,0]]],"total_cube_count":13}],"canvas_size":[619,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0611","image_path":"images/combination3d_0611.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0611_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0611_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0611_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0611_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0611_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":611,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[4,0,0],[4,0,1],[4,0,2],[4,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,1],[2,0,2],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,2],[1,0,3]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[2,1,0],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,2],[1,2,1],[1,2,2],[2,0,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":14}],"canvas_size":[578,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0612","image_path":"images/combination3d_0612.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0612_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0612_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0612_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0612_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0612_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":612,"target_cube_count":14,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,1,2],[4,1,0],[4,1,1],[5,1,0],[5,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1],[3,1,1],[4,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,2,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14}],"canvas_size":[585,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0613","image_path":"images/combination3d_0613.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0613_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0613_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0613_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_0613_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0613_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":613,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,2],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,2,0],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[582,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0614","image_path":"images/combination3d_0614.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0614_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0614_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0614_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_0614_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0614_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":614,"target_cube_count":12,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,3,0],[1,4,0],[1,4,1],[2,1,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[579,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0615","image_path":"images/combination3d_0615.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0615_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0615_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0615_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0615_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0615_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":615,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[553,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0616","image_path":"images/combination3d_0616.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0616_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0616_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0616_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0616_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0616_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":616,"target_cube_count":11,"target_cubes":[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,2,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2]]],"total_cube_count":14}],"canvas_size":[610,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0617","image_path":"images/combination3d_0617.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0617_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0617_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0617_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_0617_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0617_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":617,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[608,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0618","image_path":"images/combination3d_0618.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0618_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0618_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0618_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0618_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0618_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":618,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[615,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0619","image_path":"images/combination3d_0619.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0619_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0619_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0619_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0619_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0619_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":619,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[1,3,1]],[[0,0,1],[0,0,2],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,2,1],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":12}],"canvas_size":[578,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0620","image_path":"images/combination3d_0620.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0620_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0620_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0620_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0620_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0620_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":620,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,1,1]]],"total_cube_count":12}],"canvas_size":[590,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0621","image_path":"images/combination3d_0621.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0621_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0621_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0621_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0621_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0621_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":621,"target_cube_count":12,"target_cubes":[[0,3,0],[0,4,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,2],[1,2,2],[2,0,2],[2,0,3],[2,1,1],[2,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,1],[3,0,0],[4,0,0],[4,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,1],[3,0,0],[4,0,0],[4,0,1],[4,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,2,0],[1,2,1],[1,4,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[587,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0622","image_path":"images/combination3d_0622.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0622_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0622_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0622_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0622_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0622_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":622,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,0,0],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[555,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0623","image_path":"images/combination3d_0623.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0623_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0623_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0623_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_0623_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0623_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":623,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8}],"canvas_size":[574,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0624","image_path":"images/combination3d_0624.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0624_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0624_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0624_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0624_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0624_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":624,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[0,2,2],[1,0,1],[1,1,3],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[602,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0625","image_path":"images/combination3d_0625.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0625_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0625_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0625_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0625_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0625_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":625,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,0,2],[3,0,3],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,2]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2]]],"total_cube_count":8}],"canvas_size":[596,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0626","image_path":"images/combination3d_0626.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0626_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0626_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0626_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0626_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0626_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":626,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,2],[2,0,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":12}],"canvas_size":[582,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0627","image_path":"images/combination3d_0627.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0627_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0627_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0627_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0627_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_0627_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":627,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[600,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0628","image_path":"images/combination3d_0628.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0628_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0628_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0628_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0628_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0628_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":628,"target_cube_count":12,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,1],[1,1,1],[1,2,1],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[556,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0629","image_path":"images/combination3d_0629.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0629_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0629_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0629_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0629_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0629_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":629,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[608,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0630","image_path":"images/combination3d_0630.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0630_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0630_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0630_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0630_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0630_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":630,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,2,0],[3,0,0],[4,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[586,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0631","image_path":"images/combination3d_0631.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0631_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0631_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0631_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0631_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0631_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":631,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12}],"canvas_size":[596,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0632","image_path":"images/combination3d_0632.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0632_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0632_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0632_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0632_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0632_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":632,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,3],[1,1,1],[1,1,2],[1,1,3],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,2,1],[3,2,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":15}],"canvas_size":[555,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0633","image_path":"images/combination3d_0633.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0633_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0633_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0633_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0633_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0633_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":633,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":13}],"canvas_size":[566,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0634","image_path":"images/combination3d_0634.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0634_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0634_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0634_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0634_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0634_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":634,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[0,3,1],[1,0,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":15}],"canvas_size":[594,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0635","image_path":"images/combination3d_0635.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0635_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0635_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0635_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0635_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_0635_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":635,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[1,3,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0],[2,3,0],[3,2,0],[3,3,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,0,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,3,3]]],"total_cube_count":14}],"canvas_size":[575,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0636","image_path":"images/combination3d_0636.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0636_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0636_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0636_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_0636_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0636_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":636,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,2,1],[1,3,1],[2,2,1],[2,3,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":10}],"canvas_size":[612,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0637","image_path":"images/combination3d_0637.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0637_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0637_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0637_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0637_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_0637_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":637,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[2,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,1],[1,2,0],[1,3,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[2,2,1]]],"total_cube_count":14}],"canvas_size":[579,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0638","image_path":"images/combination3d_0638.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0638_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0638_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0638_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0638_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0638_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":638,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,3],[1,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,2,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13}],"canvas_size":[600,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0639","image_path":"images/combination3d_0639.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0639_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0639_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0639_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0639_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0639_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":639,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,2,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[552,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0640","image_path":"images/combination3d_0640.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0640_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0640_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0640_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0640_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0640_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":640,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[598,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0641","image_path":"images/combination3d_0641.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0641_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0641_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0641_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0641_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0641_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":641,"target_cube_count":8,"target_cubes":[[0,3,0],[1,0,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,1],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[582,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0642","image_path":"images/combination3d_0642.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0642_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0642_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0642_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0642_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0642_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":642,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,1],[1,2,1],[1,3,1],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,1],[1,1,2],[1,1,3],[2,0,2],[2,1,1],[2,1,2],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,2,1],[2,3,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11}],"canvas_size":[620,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0643","image_path":"images/combination3d_0643.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0643_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0643_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0643_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0643_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0643_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":643,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":11}],"canvas_size":[612,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0644","image_path":"images/combination3d_0644.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0644_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0644_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0644_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0644_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0644_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":644,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[575,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0645","image_path":"images/combination3d_0645.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0645_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0645_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0645_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0645_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0645_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":645,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,1],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,2,0],[2,2,0]]],"total_cube_count":12}],"canvas_size":[591,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0646","image_path":"images/combination3d_0646.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0646_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0646_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0646_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0646_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0646_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":646,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,2],[0,1,3],[0,2,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,2],[0,1,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":13}],"canvas_size":[619,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0647","image_path":"images/combination3d_0647.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0647_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0647_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0647_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0647_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0647_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":647,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[572,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0648","image_path":"images/combination3d_0648.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0648_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0648_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0648_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0648_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0648_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":648,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[595,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0649","image_path":"images/combination3d_0649.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0649_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0649_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0649_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0649_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0649_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":649,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,2,0],[2,0,0],[2,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,3,0],[2,3,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":13}],"canvas_size":[590,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0650","image_path":"images/combination3d_0650.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0650_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0650_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0650_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0650_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0650_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":650,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,2,1],[2,2,1],[3,2,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12}],"canvas_size":[555,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0651","image_path":"images/combination3d_0651.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0651_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0651_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0651_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0651_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0651_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":651,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":12}],"canvas_size":[568,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0652","image_path":"images/combination3d_0652.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0652_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0652_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0652_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0652_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0652_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":652,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,0],[0,2,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,2],[1,0,2],[1,1,1],[1,1,2],[1,1,3],[1,2,2]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,2],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[613,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0653","image_path":"images/combination3d_0653.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0653_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0653_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0653_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0653_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0653_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":653,"target_cube_count":12,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[599,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0654","image_path":"images/combination3d_0654.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0654_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0654_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0654_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0654_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0654_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":654,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[554,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0655","image_path":"images/combination3d_0655.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0655_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0655_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0655_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0655_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0655_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":655,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[607,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0656","image_path":"images/combination3d_0656.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0656_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0656_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0656_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,4","question_id":"combination3d_0656_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0656_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":656,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10}],"canvas_size":[590,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0657","image_path":"images/combination3d_0657.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0657_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0657_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0657_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0657_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0657_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":657,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8}],"canvas_size":[569,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0658","image_path":"images/combination3d_0658.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0658_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0658_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0658_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_0658_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0658_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":658,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":12}],"canvas_size":[587,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0659","image_path":"images/combination3d_0659.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0659_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0659_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0659_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0659_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0659_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":659,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,0,2],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[552,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0660","image_path":"images/combination3d_0660.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0660_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0660_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0660_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0660_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0660_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":660,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":12}],"canvas_size":[572,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0661","image_path":"images/combination3d_0661.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0661_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0661_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0661_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0661_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0661_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":661,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[564,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0662","image_path":"images/combination3d_0662.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0662_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0662_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0662_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0662_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0662_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":662,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[565,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0663","image_path":"images/combination3d_0663.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0663_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0663_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0663_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0663_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0663_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":663,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[4,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[615,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0664","image_path":"images/combination3d_0664.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0664_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0664_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0664_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0664_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0664_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":664,"target_cube_count":11,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,0,0],[3,1,0],[4,0,0],[5,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,2,0],[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,1],[0,3,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9}],"canvas_size":[616,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0665","image_path":"images/combination3d_0665.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0665_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0665_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0665_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0665_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0665_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":665,"target_cube_count":9,"target_cubes":[[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[608,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0666","image_path":"images/combination3d_0666.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0666_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0666_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0666_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0666_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0666_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":666,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0],[3,1,1],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0],[3,3,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,3],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,1],[3,0,2]]],"total_cube_count":11}],"canvas_size":[563,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0667","image_path":"images/combination3d_0667.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0667_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0667_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0667_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0667_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0667_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":667,"target_cube_count":11,"target_cubes":[[0,3,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8}],"canvas_size":[609,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0668","image_path":"images/combination3d_0668.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0668_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0668_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0668_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0668_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0668_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":668,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12}],"canvas_size":[588,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0669","image_path":"images/combination3d_0669.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0669_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0669_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0669_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0669_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0669_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":669,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[595,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0670","image_path":"images/combination3d_0670.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0670_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0670_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0670_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0670_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0670_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":670,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,1],[1,1,2],[1,2,1],[2,0,0],[2,0,1],[2,1,1],[2,2,1],[2,3,1],[3,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,2]]],"total_cube_count":11}],"canvas_size":[567,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0671","image_path":"images/combination3d_0671.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0671_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0671_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0671_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0671_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0671_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":671,"target_cube_count":11,"target_cubes":[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[552,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0672","image_path":"images/combination3d_0672.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0672_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0672_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0672_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_0672_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0672_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":672,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11}],"canvas_size":[617,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0673","image_path":"images/combination3d_0673.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0673_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0673_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0673_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0673_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0673_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":673,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,1]]],"total_cube_count":8}],"canvas_size":[601,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0674","image_path":"images/combination3d_0674.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0674_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0674_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0674_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0674_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0674_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":674,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[576,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0675","image_path":"images/combination3d_0675.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0675_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0675_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0675_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0675_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0675_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":675,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,1],[0,2,2],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,3,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[0,1,3],[0,1,4]],[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,2,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,4,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,2,0]]],"total_cube_count":14}],"canvas_size":[553,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0676","image_path":"images/combination3d_0676.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0676_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0676_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0676_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_0676_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0676_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":676,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[1,5,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8}],"canvas_size":[558,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0677","image_path":"images/combination3d_0677.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0677_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0677_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0677_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0677_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0677_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":677,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[564,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0678","image_path":"images/combination3d_0678.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0678_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0678_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0678_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_0678_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0678_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":678,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,1]]],"total_cube_count":11}],"canvas_size":[618,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0679","image_path":"images/combination3d_0679.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0679_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0679_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0679_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0679_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0679_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":679,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[3,0,1],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[612,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0680","image_path":"images/combination3d_0680.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0680_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0680_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0680_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0680_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0680_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":680,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[602,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0681","image_path":"images/combination3d_0681.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0681_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0681_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0681_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,5","question_id":"combination3d_0681_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0681_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":681,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[617,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0682","image_path":"images/combination3d_0682.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0682_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0682_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0682_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0682_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0682_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":682,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[600,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0683","image_path":"images/combination3d_0683.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0683_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0683_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0683_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0683_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0683_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":683,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1],[2,1,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12}],"canvas_size":[599,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0684","image_path":"images/combination3d_0684.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0684_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0684_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0684_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0684_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0684_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":684,"target_cube_count":12,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[588,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0685","image_path":"images/combination3d_0685.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0685_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0685_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0685_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0685_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0685_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":685,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[1,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[617,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0686","image_path":"images/combination3d_0686.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0686_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0686_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0686_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0686_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0686_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":686,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[2,0,1],[2,1,0],[2,1,1],[2,1,3],[2,2,3]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[0,2,3]],[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14}],"canvas_size":[601,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0687","image_path":"images/combination3d_0687.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0687_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0687_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0687_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0687_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0687_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":687,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,1,2],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[584,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0688","image_path":"images/combination3d_0688.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0688_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0688_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0688_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_0688_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0688_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":688,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[570,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0689","image_path":"images/combination3d_0689.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0689_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0689_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0689_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_0689_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0689_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":689,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[591,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0690","image_path":"images/combination3d_0690.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0690_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0690_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0690_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0690_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0690_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":690,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9}],"canvas_size":[569,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0691","image_path":"images/combination3d_0691.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0691_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0691_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0691_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0691_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0691_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":691,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[553,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0692","image_path":"images/combination3d_0692.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0692_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0692_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0692_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0692_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0692_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":692,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,4,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,1,1],[1,1,1],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,4,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[611,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0693","image_path":"images/combination3d_0693.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0693_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0693_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0693_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0693_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0693_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":693,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,3,0],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[610,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0694","image_path":"images/combination3d_0694.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0694_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0694_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0694_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_0694_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0694_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":694,"target_cube_count":10,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[592,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0695","image_path":"images/combination3d_0695.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0695_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0695_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0695_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0695_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0695_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":695,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[571,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0696","image_path":"images/combination3d_0696.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0696_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0696_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0696_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0696_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0696_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":696,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[567,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0697","image_path":"images/combination3d_0697.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0697_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0697_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0697_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0697_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0697_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":697,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]]],"total_cube_count":12}],"canvas_size":[596,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0698","image_path":"images/combination3d_0698.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0698_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0698_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0698_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0698_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0698_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":698,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[1,0,3],[2,0,1],[2,0,2],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,1]],[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]]],"total_cube_count":14}],"canvas_size":[596,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0699","image_path":"images/combination3d_0699.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0699_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0699_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0699_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0699_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0699_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":699,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1],[3,1,2],[3,1,3],[4,1,0],[4,1,1],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,3,0],[1,3,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9}],"canvas_size":[571,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0700","image_path":"images/combination3d_0700.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0700_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0700_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0700_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0700_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0700_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":700,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":8}],"canvas_size":[585,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0701","image_path":"images/combination3d_0701.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0701_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0701_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0701_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0701_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0701_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":701,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[2,0,2],[3,0,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]]],"total_cube_count":9}],"canvas_size":[563,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0702","image_path":"images/combination3d_0702.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0702_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0702_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0702_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0702_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0702_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":702,"target_cube_count":8,"target_cubes":[[0,3,0],[1,3,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[556,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0703","image_path":"images/combination3d_0703.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0703_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0703_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0703_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0703_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0703_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":703,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,3],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[597,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0704","image_path":"images/combination3d_0704.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0704_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0704_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0704_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0704_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0704_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":704,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,3,0],[3,3,1],[3,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2],[3,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[583,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0705","image_path":"images/combination3d_0705.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0705_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0705_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0705_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0705_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0705_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":705,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,2,3],[1,3,3]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[4,0,0],[4,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[583,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0706","image_path":"images/combination3d_0706.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0706_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0706_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0706_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0706_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0706_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":706,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":13}],"canvas_size":[552,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0707","image_path":"images/combination3d_0707.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0707_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0707_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0707_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0707_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0707_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":707,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,3,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,3,0]]],"total_cube_count":14}],"canvas_size":[565,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0708","image_path":"images/combination3d_0708.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0708_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0708_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0708_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0708_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0708_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":708,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,3,0],[3,3,1],[3,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,2],[0,2,2],[1,0,1]]],"total_cube_count":10}],"canvas_size":[618,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0709","image_path":"images/combination3d_0709.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0709_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0709_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0709_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0709_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0709_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":709,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[598,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0710","image_path":"images/combination3d_0710.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0710_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0710_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0710_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0710_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0710_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":710,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2],[1,2,3],[2,0,2],[2,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[612,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0711","image_path":"images/combination3d_0711.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0711_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0711_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0711_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0711_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0711_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":711,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,3,0],[1,3,1],[2,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[587,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0712","image_path":"images/combination3d_0712.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0712_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0712_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0712_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0712_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0712_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":712,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,3,1],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[599,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0713","image_path":"images/combination3d_0713.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0713_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0713_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0713_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0713_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0713_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":713,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]]],"total_cube_count":11}],"canvas_size":[564,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0714","image_path":"images/combination3d_0714.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0714_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0714_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0714_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0714_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0714_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":714,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,2,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9}],"canvas_size":[615,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0715","image_path":"images/combination3d_0715.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0715_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0715_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0715_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_0715_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0715_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":715,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,0,2],[2,1,1],[2,2,1],[3,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[570,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0716","image_path":"images/combination3d_0716.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0716_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0716_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0716_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0716_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0716_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":716,"target_cube_count":13,"target_cubes":[[0,0,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1],[3,0,1],[3,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[4,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[580,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0717","image_path":"images/combination3d_0717.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0717_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0717_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0717_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0717_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0717_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":717,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2],[2,0,3],[2,0,4]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[583,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0718","image_path":"images/combination3d_0718.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0718_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0718_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0718_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0718_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_0718_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":718,"target_cube_count":13,"target_cubes":[[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[1,3,3],[1,3,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8}],"canvas_size":[585,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0719","image_path":"images/combination3d_0719.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0719_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0719_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0719_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0719_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0719_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":719,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0],[4,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,1],[3,1,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,4,0],[0,4,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,4,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[569,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0720","image_path":"images/combination3d_0720.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0720_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0720_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0720_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0720_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0720_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":720,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11}],"canvas_size":[569,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0721","image_path":"images/combination3d_0721.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0721_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0721_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0721_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0721_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0721_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":721,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,0,2],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[569,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0722","image_path":"images/combination3d_0722.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0722_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0722_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0722_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0722_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0722_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":722,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[619,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0723","image_path":"images/combination3d_0723.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0723_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0723_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0723_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0723_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0723_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":723,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[587,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0724","image_path":"images/combination3d_0724.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0724_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0724_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0724_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0724_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0724_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":724,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,2,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8}],"canvas_size":[560,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0725","image_path":"images/combination3d_0725.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0725_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0725_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0725_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0725_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0725_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":725,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[583,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0726","image_path":"images/combination3d_0726.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0726_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0726_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0726_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_0726_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0726_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":726,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9}],"canvas_size":[617,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0727","image_path":"images/combination3d_0727.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0727_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0727_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0727_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0727_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0727_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":727,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,2,3],[1,3,0],[1,3,1],[1,3,2],[1,3,3],[2,3,0],[2,3,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[1,3,2],[2,0,1],[2,1,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0]]],"total_cube_count":14}],"canvas_size":[555,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0728","image_path":"images/combination3d_0728.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0728_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0728_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0728_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0728_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0728_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":728,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,2,0]]],"total_cube_count":10}],"canvas_size":[591,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0729","image_path":"images/combination3d_0729.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0729_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0729_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0729_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0729_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0729_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":729,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,1],[1,1,2]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":13}],"canvas_size":[588,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0730","image_path":"images/combination3d_0730.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0730_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0730_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0730_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0730_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0730_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":730,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[2,1,0],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,1],[0,3,2]]],"total_cube_count":12}],"canvas_size":[558,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0731","image_path":"images/combination3d_0731.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0731_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0731_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0731_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0731_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0731_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":731,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,2],[0,1,2],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[565,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0732","image_path":"images/combination3d_0732.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0732_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0732_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0732_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0732_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0732_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":732,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14}],"canvas_size":[603,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0733","image_path":"images/combination3d_0733.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0733_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0733_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0733_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0733_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0733_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":733,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[2,3,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[593,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0734","image_path":"images/combination3d_0734.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0734_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0734_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0734_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0734_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0734_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":734,"target_cube_count":10,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[604,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0735","image_path":"images/combination3d_0735.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0735_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0735_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0735_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_0735_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0735_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":735,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":8}],"canvas_size":[582,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0736","image_path":"images/combination3d_0736.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0736_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0736_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0736_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0736_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,5","question_id":"combination3d_0736_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":736,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10}],"canvas_size":[550,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0737","image_path":"images/combination3d_0737.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0737_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0737_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0737_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0737_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0737_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":737,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,2]]],"total_cube_count":10}],"canvas_size":[570,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0738","image_path":"images/combination3d_0738.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0738_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0738_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0738_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0738_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0738_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":738,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,0,0],[1,1,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,1],[1,2,1],[1,3,1],[1,3,2],[2,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[2,0,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[574,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0739","image_path":"images/combination3d_0739.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0739_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0739_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0739_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0739_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0739_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":739,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0]]],"total_cube_count":14}],"canvas_size":[555,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0740","image_path":"images/combination3d_0740.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0740_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0740_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0740_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0740_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0740_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":740,"target_cube_count":14,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[3,0,0],[3,0,1],[3,0,2],[3,0,3],[4,0,0],[4,0,1],[4,0,2],[4,0,3],[5,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[1,1,2],[2,0,1],[2,0,2],[2,1,1],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]]],"total_cube_count":13}],"canvas_size":[578,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0741","image_path":"images/combination3d_0741.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0741_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0741_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0741_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0741_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0741_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":741,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0],[2,3,0],[2,4,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0],[2,3,0],[2,4,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[4,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,1]]],"total_cube_count":9}],"canvas_size":[603,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0742","image_path":"images/combination3d_0742.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0742_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0742_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0742_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0742_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0742_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":742,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[586,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0743","image_path":"images/combination3d_0743.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0743_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0743_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0743_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0743_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0743_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":743,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12}],"canvas_size":[589,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0744","image_path":"images/combination3d_0744.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0744_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0744_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0744_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_0744_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0744_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":744,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,1],[1,2,2],[2,0,2],[2,1,2],[2,2,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14}],"canvas_size":[578,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0745","image_path":"images/combination3d_0745.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0745_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0745_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0745_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0745_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0745_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":745,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,3,0],[2,3,1],[2,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]]],"total_cube_count":9}],"canvas_size":[604,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0746","image_path":"images/combination3d_0746.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0746_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0746_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0746_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0746_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0746_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":746,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,2,0],[1,2,1],[2,2,1]],[[0,2,0],[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,2,1],[2,2,2],[2,3,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0]]],"total_cube_count":14}],"canvas_size":[588,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0747","image_path":"images/combination3d_0747.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0747_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0747_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0747_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0747_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_0747_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":747,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[559,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0748","image_path":"images/combination3d_0748.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0748_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0748_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0748_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0748_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0748_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":748,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":15}],"canvas_size":[608,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0749","image_path":"images/combination3d_0749.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0749_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0749_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0749_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_0749_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0749_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":749,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":10}],"canvas_size":[591,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0750","image_path":"images/combination3d_0750.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0750_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0750_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0750_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_0750_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0750_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":750,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[616,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0751","image_path":"images/combination3d_0751.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0751_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0751_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0751_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0751_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0751_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":751,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8}],"canvas_size":[616,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0752","image_path":"images/combination3d_0752.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0752_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0752_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0752_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0752_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0752_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":752,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,0,2],[2,0,3],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":15}],"canvas_size":[596,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0753","image_path":"images/combination3d_0753.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0753_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0753_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0753_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0753_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0753_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":753,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,1,2],[2,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[572,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0754","image_path":"images/combination3d_0754.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0754_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0754_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0754_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0754_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0754_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":754,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,3,0],[1,4,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[616,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0755","image_path":"images/combination3d_0755.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0755_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0755_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0755_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0755_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0755_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":755,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,2],[0,1,3],[0,1,4],[0,2,4],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[608,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0756","image_path":"images/combination3d_0756.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0756_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0756_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0756_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0756_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0756_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":756,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[2,0,1],[2,1,1],[2,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[3,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[600,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0757","image_path":"images/combination3d_0757.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0757_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0757_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0757_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0757_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0757_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":757,"target_cube_count":9,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[3,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[0,2,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[0,2,1],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":15}],"canvas_size":[592,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0758","image_path":"images/combination3d_0758.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0758_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0758_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0758_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0758_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_0758_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":758,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1],[2,4,0],[2,4,1],[2,5,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8}],"canvas_size":[557,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0759","image_path":"images/combination3d_0759.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0759_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0759_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0759_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0759_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0759_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":759,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,2,0],[1,2,1],[1,3,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,2,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[567,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0760","image_path":"images/combination3d_0760.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0760_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0760_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0760_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0760_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0760_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":760,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,1],[1,1,3]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,1,1],[1,2,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,1]],[[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":15}],"canvas_size":[578,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0761","image_path":"images/combination3d_0761.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0761_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0761_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0761_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0761_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_0761_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":761,"target_cube_count":14,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1],[3,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[597,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0762","image_path":"images/combination3d_0762.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0762_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0762_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0762_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0762_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0762_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":762,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[553,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0763","image_path":"images/combination3d_0763.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0763_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0763_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0763_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0763_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0763_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":763,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0],[4,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,2]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0],[4,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[570,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0764","image_path":"images/combination3d_0764.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0764_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0764_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0764_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0764_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0764_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":764,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[2,0,1]]],"total_cube_count":10}],"canvas_size":[554,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0765","image_path":"images/combination3d_0765.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0765_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0765_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0765_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0765_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0765_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":765,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[2,1,2],[3,0,1],[3,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,1],[1,1,2],[1,2,2],[1,2,3]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,1],[1,1,2],[1,2,2],[1,2,3],[1,3,2]]],"total_cube_count":15}],"canvas_size":[585,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0766","image_path":"images/combination3d_0766.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0766_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0766_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0766_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0766_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0766_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":766,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,2],[3,0,2]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,0],[2,2,1],[3,1,1],[4,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[1,4,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[1,4,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[563,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0767","image_path":"images/combination3d_0767.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0767_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0767_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0767_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0767_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0767_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":767,"target_cube_count":13,"target_cubes":[[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[3,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[3,0,0]]],"total_cube_count":11}],"canvas_size":[561,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0768","image_path":"images/combination3d_0768.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0768_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0768_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0768_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0768_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0768_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":768,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]]],"total_cube_count":13}],"canvas_size":[551,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0769","image_path":"images/combination3d_0769.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0769_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0769_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0769_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0769_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0769_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":769,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[2,1,3],[3,1,1],[3,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,1],[3,1,1],[3,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[598,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0770","image_path":"images/combination3d_0770.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0770_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0770_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0770_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0770_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0770_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":770,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":10}],"canvas_size":[598,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0771","image_path":"images/combination3d_0771.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0771_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0771_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0771_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0771_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0771_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":771,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,1]],[[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,1,1],[1,1,2],[2,1,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":14}],"canvas_size":[563,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0772","image_path":"images/combination3d_0772.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0772_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0772_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0772_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0772_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0772_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":772,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13}],"canvas_size":[572,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0773","image_path":"images/combination3d_0773.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0773_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0773_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0773_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0773_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0773_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":773,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1]]],"total_cube_count":8}],"canvas_size":[588,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0774","image_path":"images/combination3d_0774.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0774_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0774_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0774_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_0774_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0774_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":774,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,2,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":8}],"canvas_size":[612,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0775","image_path":"images/combination3d_0775.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0775_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0775_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0775_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0775_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0775_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":775,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":12}],"canvas_size":[607,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0776","image_path":"images/combination3d_0776.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0776_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0776_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0776_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_0776_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0776_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":776,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0],[4,1,0],[4,1,1],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,2],[0,2,2],[1,0,1],[1,0,2],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12}],"canvas_size":[579,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0777","image_path":"images/combination3d_0777.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0777_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0777_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0777_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0777_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0777_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":777,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[555,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0778","image_path":"images/combination3d_0778.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0778_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0778_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0778_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_0778_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0778_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":778,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":15}],"canvas_size":[619,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0779","image_path":"images/combination3d_0779.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0779_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0779_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0779_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_0779_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0779_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":779,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[0,1,3],[0,2,3],[1,1,2],[1,2,2],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,1],[2,2,2],[3,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,3,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[575,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0780","image_path":"images/combination3d_0780.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0780_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0780_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0780_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_0780_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0780_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":780,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":12}],"canvas_size":[577,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0781","image_path":"images/combination3d_0781.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0781_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0781_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0781_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0781_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0781_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":781,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,1],[2,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11}],"canvas_size":[564,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0782","image_path":"images/combination3d_0782.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0782_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0782_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0782_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0782_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0782_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":782,"target_cube_count":10,"target_cubes":[[0,1,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[1,5,0],[1,5,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,1],[0,3,2],[0,3,3],[0,3,4]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[3,1,1],[4,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[620,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0783","image_path":"images/combination3d_0783.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0783_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0783_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0783_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0783_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0783_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":783,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8}],"canvas_size":[605,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0784","image_path":"images/combination3d_0784.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0784_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0784_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0784_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0784_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0784_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":784,"target_cube_count":8,"target_cubes":[[0,0,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[615,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0785","image_path":"images/combination3d_0785.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0785_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0785_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0785_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0785_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0785_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":785,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[597,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0786","image_path":"images/combination3d_0786.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0786_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0786_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0786_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0786_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0786_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":786,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1],[3,1,2],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":13}],"canvas_size":[589,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0787","image_path":"images/combination3d_0787.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0787_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0787_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0787_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0787_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0787_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":787,"target_cube_count":13,"target_cubes":[[0,4,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":14}],"canvas_size":[611,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0788","image_path":"images/combination3d_0788.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0788_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0788_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0788_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0788_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0788_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":788,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[3,0,0],[3,0,1],[3,0,2],[3,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,0]]],"total_cube_count":13}],"canvas_size":[611,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0789","image_path":"images/combination3d_0789.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0789_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0789_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0789_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_0789_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0789_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":789,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1]]],"total_cube_count":13}],"canvas_size":[587,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0790","image_path":"images/combination3d_0790.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0790_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0790_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0790_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0790_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0790_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":790,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[576,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0791","image_path":"images/combination3d_0791.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0791_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0791_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0791_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0791_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0791_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":791,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[2,0,1],[2,0,2],[3,0,2]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[3,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14}],"canvas_size":[616,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0792","image_path":"images/combination3d_0792.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0792_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0792_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0792_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0792_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0792_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":792,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1],[3,0,2],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13}],"canvas_size":[584,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0793","image_path":"images/combination3d_0793.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0793_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0793_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0793_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0793_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0793_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":793,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[589,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0794","image_path":"images/combination3d_0794.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0794_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0794_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0794_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0794_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0794_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":794,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,0]]],"total_cube_count":11}],"canvas_size":[601,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0795","image_path":"images/combination3d_0795.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0795_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0795_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0795_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0795_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0795_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":795,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[606,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0796","image_path":"images/combination3d_0796.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0796_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0796_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0796_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0796_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0796_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":796,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8}],"canvas_size":[600,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0797","image_path":"images/combination3d_0797.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0797_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0797_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0797_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0797_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0797_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":797,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[1,0,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[2,0,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[2,0,1],[3,0,0],[3,0,1],[4,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[602,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0798","image_path":"images/combination3d_0798.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0798_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0798_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0798_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0798_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_0798_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":798,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,1,3],[0,2,3],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]],[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":13}],"canvas_size":[574,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0799","image_path":"images/combination3d_0799.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0799_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0799_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0799_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0799_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0799_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":799,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,1,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[613,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0800","image_path":"images/combination3d_0800.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0800_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0800_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0800_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0800_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0800_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":800,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[4,0,1]]],"total_cube_count":10}],"canvas_size":[563,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0801","image_path":"images/combination3d_0801.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0801_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0801_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0801_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0801_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0801_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":801,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[620,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0802","image_path":"images/combination3d_0802.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0802_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0802_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0802_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,5","question_id":"combination3d_0802_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0802_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":802,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,3,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11}],"canvas_size":[563,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0803","image_path":"images/combination3d_0803.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0803_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0803_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0803_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0803_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0803_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":803,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[611,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0804","image_path":"images/combination3d_0804.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0804_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0804_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0804_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0804_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0804_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":804,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,1,1],[3,0,1],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,1]]],"total_cube_count":14}],"canvas_size":[613,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0805","image_path":"images/combination3d_0805.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0805_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0805_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0805_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0805_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_0805_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":805,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,2]]],"total_cube_count":12}],"canvas_size":[608,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0806","image_path":"images/combination3d_0806.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0806_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0806_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0806_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0806_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0806_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":806,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[597,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0807","image_path":"images/combination3d_0807.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0807_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0807_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0807_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0807_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0807_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":807,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0],[2,2,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,3,1],[0,3,2],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,1],[1,3,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[596,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0808","image_path":"images/combination3d_0808.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0808_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0808_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0808_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0808_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0808_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":808,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[556,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0809","image_path":"images/combination3d_0809.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0809_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0809_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0809_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0809_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0809_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":809,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]]],"total_cube_count":8}],"canvas_size":[609,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0810","image_path":"images/combination3d_0810.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0810_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0810_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0810_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0810_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0810_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":810,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[561,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0811","image_path":"images/combination3d_0811.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0811_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0811_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0811_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0811_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0811_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":811,"target_cube_count":12,"target_cubes":[[0,2,0],[0,4,0],[0,4,1],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12}],"canvas_size":[554,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0812","image_path":"images/combination3d_0812.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0812_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0812_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0812_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0812_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0812_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":812,"target_cube_count":12,"target_cubes":[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15}],"canvas_size":[566,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0813","image_path":"images/combination3d_0813.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0813_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0813_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0813_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0813_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0813_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":813,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[567,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0814","image_path":"images/combination3d_0814.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0814_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0814_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0814_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0814_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_0814_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":814,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,2,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[551,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0815","image_path":"images/combination3d_0815.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0815_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0815_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0815_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0815_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0815_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":815,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[570,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0816","image_path":"images/combination3d_0816.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0816_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0816_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0816_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0816_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0816_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":816,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[566,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0817","image_path":"images/combination3d_0817.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0817_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0817_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0817_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0817_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0817_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":817,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[610,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0818","image_path":"images/combination3d_0818.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0818_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0818_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0818_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_0818_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0818_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":818,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0],[4,2,0],[4,3,0],[5,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1],[2,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[596,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0819","image_path":"images/combination3d_0819.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0819_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0819_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0819_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0819_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_0819_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":819,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,2,1],[3,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[577,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0820","image_path":"images/combination3d_0820.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0820_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0820_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0820_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0820_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0820_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":820,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[3,0,0],[3,1,0],[3,1,1],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[2,3,0],[2,3,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,0],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":15}],"canvas_size":[612,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0821","image_path":"images/combination3d_0821.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0821_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0821_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0821_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0821_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0821_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":821,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,2],[1,2,3],[2,1,2]]],"total_cube_count":10}],"canvas_size":[564,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0822","image_path":"images/combination3d_0822.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0822_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0822_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0822_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0822_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0822_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":822,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,1]]],"total_cube_count":14}],"canvas_size":[593,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0823","image_path":"images/combination3d_0823.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0823_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0823_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0823_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0823_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0823_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":823,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,1],[2,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10}],"canvas_size":[568,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0824","image_path":"images/combination3d_0824.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0824_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0824_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0824_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0824_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0824_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":824,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[3,1,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[584,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0825","image_path":"images/combination3d_0825.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0825_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0825_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0825_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0825_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0825_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":825,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14}],"canvas_size":[620,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0826","image_path":"images/combination3d_0826.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0826_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0826_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0826_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0826_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0826_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":826,"target_cube_count":13,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1],[3,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[595,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0827","image_path":"images/combination3d_0827.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0827_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0827_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0827_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0827_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0827_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":827,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[575,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0828","image_path":"images/combination3d_0828.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0828_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0828_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0828_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_0828_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0828_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":828,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11}],"canvas_size":[576,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0829","image_path":"images/combination3d_0829.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0829_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0829_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0829_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0829_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0829_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":829,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0],[2,3,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,1,5],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[3,1,1],[4,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,2]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[563,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0830","image_path":"images/combination3d_0830.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0830_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0830_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0830_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0830_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0830_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":830,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[2,0,2],[2,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,2],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[570,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0831","image_path":"images/combination3d_0831.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0831_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0831_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0831_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0831_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0831_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":831,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[619,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0832","image_path":"images/combination3d_0832.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0832_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0832_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0832_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0832_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0832_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":832,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[587,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0833","image_path":"images/combination3d_0833.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0833_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0833_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0833_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0833_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0833_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":833,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[587,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0834","image_path":"images/combination3d_0834.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0834_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0834_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0834_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0834_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_0834_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":834,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[577,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0835","image_path":"images/combination3d_0835.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0835_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0835_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0835_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0835_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0835_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":835,"target_cube_count":8,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12}],"canvas_size":[602,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0836","image_path":"images/combination3d_0836.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0836_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0836_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0836_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0836_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0836_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":836,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":8}],"canvas_size":[583,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0837","image_path":"images/combination3d_0837.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0837_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0837_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0837_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_0837_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0837_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":837,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[615,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0838","image_path":"images/combination3d_0838.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0838_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0838_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0838_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0838_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0838_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":838,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[564,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0839","image_path":"images/combination3d_0839.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0839_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0839_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0839_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0839_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0839_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":839,"target_cube_count":10,"target_cubes":[[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,2],[2,1,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[576,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0840","image_path":"images/combination3d_0840.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0840_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0840_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0840_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0840_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0840_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":840,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,2],[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,3]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[599,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0841","image_path":"images/combination3d_0841.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0841_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0841_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0841_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0841_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_0841_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":841,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[558,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0842","image_path":"images/combination3d_0842.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0842_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0842_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0842_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0842_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0842_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":842,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[614,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0843","image_path":"images/combination3d_0843.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0843_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0843_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0843_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0843_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0843_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":843,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[1,3,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9}],"canvas_size":[616,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0844","image_path":"images/combination3d_0844.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0844_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0844_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0844_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0844_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0844_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":844,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14}],"canvas_size":[557,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0845","image_path":"images/combination3d_0845.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0845_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0845_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0845_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_0845_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0845_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":845,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[1,0,1],[2,0,1],[2,0,2],[2,1,1],[2,1,2],[3,0,0],[3,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[563,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0846","image_path":"images/combination3d_0846.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0846_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0846_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0846_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_0846_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0846_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":846,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[599,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0847","image_path":"images/combination3d_0847.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0847_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0847_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0847_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0847_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0847_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":847,"target_cube_count":11,"target_cubes":[[0,0,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[606,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0848","image_path":"images/combination3d_0848.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0848_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0848_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0848_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0848_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0848_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":848,"target_cube_count":11,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[550,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0849","image_path":"images/combination3d_0849.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0849_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0849_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0849_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0849_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0849_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":849,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11}],"canvas_size":[613,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0850","image_path":"images/combination3d_0850.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0850_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0850_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0850_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0850_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0850_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":850,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1]],[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3]]],"total_cube_count":10}],"canvas_size":[601,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0851","image_path":"images/combination3d_0851.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0851_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0851_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0851_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0851_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0851_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":851,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[557,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0852","image_path":"images/combination3d_0852.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0852_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0852_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0852_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0852_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0852_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":852,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,0,5],[2,0,1],[2,0,2],[2,0,3]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,2,3],[1,3,1],[1,3,2],[1,3,3]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[601,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0853","image_path":"images/combination3d_0853.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0853_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0853_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0853_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_0853_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0853_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":853,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[2,1,1],[2,1,2],[3,1,1],[3,1,2],[4,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[4,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[3,2,0],[4,1,0]]],"total_cube_count":14}],"canvas_size":[595,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0854","image_path":"images/combination3d_0854.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0854_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0854_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0854_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0854_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0854_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":854,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[581,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0855","image_path":"images/combination3d_0855.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0855_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0855_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0855_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0855_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0855_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":855,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[4,1,0],[5,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[3,1,1],[4,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[4,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[577,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0856","image_path":"images/combination3d_0856.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0856_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0856_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0856_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0856_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0856_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":856,"target_cube_count":9,"target_cubes":[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2]]],"total_cube_count":13}],"canvas_size":[611,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0857","image_path":"images/combination3d_0857.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0857_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0857_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0857_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0857_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0857_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":857,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[617,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0858","image_path":"images/combination3d_0858.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0858_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0858_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0858_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0858_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0858_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":858,"target_cube_count":8,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8}],"canvas_size":[578,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0859","image_path":"images/combination3d_0859.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0859_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0859_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0859_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0859_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0859_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":859,"target_cube_count":8,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,5,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[2,1,1],[2,2,0],[2,2,1],[2,2,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[3,0,1],[3,1,1],[4,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13}],"canvas_size":[567,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0860","image_path":"images/combination3d_0860.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0860_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0860_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0860_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0860_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_0860_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":860,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[2,2,1],[2,3,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[3,1,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":14}],"canvas_size":[607,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0861","image_path":"images/combination3d_0861.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0861_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0861_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0861_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0861_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0861_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":861,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0],[3,2,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,1]]],"total_cube_count":12}],"canvas_size":[576,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0862","image_path":"images/combination3d_0862.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0862_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0862_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0862_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0862_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0862_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":862,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,1],[1,2,1],[1,3,1],[2,2,1],[2,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,1],[1,0,1],[1,2,2],[1,3,1],[2,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[585,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0863","image_path":"images/combination3d_0863.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0863_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0863_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0863_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0863_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0863_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":863,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0]]],"total_cube_count":11}],"canvas_size":[589,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0864","image_path":"images/combination3d_0864.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0864_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0864_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0864_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0864_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0864_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":864,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[601,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0865","image_path":"images/combination3d_0865.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0865_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0865_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0865_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0865_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0865_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":865,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9}],"canvas_size":[565,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0866","image_path":"images/combination3d_0866.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0866_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0866_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0866_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0866_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0866_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":866,"target_cube_count":8,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,2,3],[1,2,1],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[3,1,0],[4,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[3,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[567,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0867","image_path":"images/combination3d_0867.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0867_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0867_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0867_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0867_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0867_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":867,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,2,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[601,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0868","image_path":"images/combination3d_0868.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0868_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0868_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0868_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0868_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0868_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":868,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,1],[2,0,2],[3,0,2],[4,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,1]]],"total_cube_count":12}],"canvas_size":[602,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0869","image_path":"images/combination3d_0869.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0869_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0869_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0869_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0869_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0869_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":869,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[581,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0870","image_path":"images/combination3d_0870.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0870_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0870_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0870_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0870_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_0870_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":870,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,2],[2,0,1],[2,1,2],[3,1,2],[4,1,2]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,1],[1,3,1],[2,2,0],[2,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,1,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":15}],"canvas_size":[594,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0871","image_path":"images/combination3d_0871.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0871_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0871_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0871_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0871_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0871_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":871,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[620,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0872","image_path":"images/combination3d_0872.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0872_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0872_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0872_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_0872_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0872_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":872,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,0,3],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,2],[1,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]]],"total_cube_count":13}],"canvas_size":[568,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0873","image_path":"images/combination3d_0873.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0873_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0873_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0873_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0873_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0873_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":873,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[616,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0874","image_path":"images/combination3d_0874.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0874_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0874_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0874_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0874_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0874_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":874,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,3],[2,0,3],[2,0,4]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,1],[0,4,1],[1,2,0],[1,3,1],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[1,3,2],[1,4,1],[2,1,1],[2,2,1],[2,2,2],[2,2,3]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[614,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0875","image_path":"images/combination3d_0875.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0875_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0875_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0875_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0875_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0875_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":875,"target_cube_count":13,"target_cubes":[[0,2,0],[1,2,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0],[3,3,1],[3,4,0],[4,1,0],[4,2,0],[4,2,1],[4,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[552,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0876","image_path":"images/combination3d_0876.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0876_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0876_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0876_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0876_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0876_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":876,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,1]]],"total_cube_count":14}],"canvas_size":[578,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0877","image_path":"images/combination3d_0877.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0877_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0877_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0877_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0877_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0877_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":877,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,3],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,2],[2,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[619,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0878","image_path":"images/combination3d_0878.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0878_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0878_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0878_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_0878_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0878_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":878,"target_cube_count":10,"target_cubes":[[0,2,0],[0,3,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":12}],"canvas_size":[559,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0879","image_path":"images/combination3d_0879.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0879_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0879_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0879_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0879_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_0879_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":879,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1],[4,0,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[563,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0880","image_path":"images/combination3d_0880.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0880_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0880_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0880_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_0880_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0880_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":880,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,2,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14}],"canvas_size":[591,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0881","image_path":"images/combination3d_0881.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0881_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0881_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0881_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0881_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0881_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":881,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,3,0],[2,3,1],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0],[4,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,3],[1,1,2],[1,1,3],[2,0,3],[2,1,3]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[551,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0882","image_path":"images/combination3d_0882.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0882_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0882_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0882_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0882_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0882_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":882,"target_cube_count":13,"target_cubes":[[0,2,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0],[3,3,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[0,2,3],[0,2,4],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[563,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0883","image_path":"images/combination3d_0883.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0883_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0883_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0883_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0883_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0883_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":883,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":13}],"canvas_size":[561,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0884","image_path":"images/combination3d_0884.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0884_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0884_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0884_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0884_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0884_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":884,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[1,2,2],[1,2,3],[2,1,0]]],"total_cube_count":14}],"canvas_size":[597,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0885","image_path":"images/combination3d_0885.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0885_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0885_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0885_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_0885_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0885_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":885,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,1],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,3,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[574,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0886","image_path":"images/combination3d_0886.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0886_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0886_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0886_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0886_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0886_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":886,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,3,2],[1,1,1],[1,3,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[613,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0887","image_path":"images/combination3d_0887.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0887_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0887_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0887_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0887_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0887_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":887,"target_cube_count":11,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,3,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[560,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0888","image_path":"images/combination3d_0888.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0888_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0888_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0888_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0888_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0888_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":888,"target_cube_count":12,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,3,0],[2,3,1],[2,4,0],[2,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":8}],"canvas_size":[579,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0889","image_path":"images/combination3d_0889.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0889_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0889_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0889_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0889_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0889_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":889,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[556,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0890","image_path":"images/combination3d_0890.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0890_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0890_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0890_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_0890_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0890_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":890,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[3,1,0]],[[0,0,1],[0,0,2],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,1],[3,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,1,0]],[[0,0,1],[0,0,2],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,2],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,1,1]]],"total_cube_count":12}],"canvas_size":[601,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0891","image_path":"images/combination3d_0891.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0891_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0891_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0891_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_0891_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0891_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":891,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,2,1],[0,3,0],[0,3,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":10}],"canvas_size":[578,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0892","image_path":"images/combination3d_0892.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0892_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0892_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0892_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0892_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0892_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":892,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[614,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0893","image_path":"images/combination3d_0893.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0893_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0893_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0893_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0893_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0893_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":893,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[606,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0894","image_path":"images/combination3d_0894.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0894_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0894_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0894_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0894_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_0894_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":894,"target_cube_count":10,"target_cubes":[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[553,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0895","image_path":"images/combination3d_0895.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0895_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0895_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0895_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0895_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0895_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":895,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":8}],"canvas_size":[575,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0896","image_path":"images/combination3d_0896.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0896_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0896_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0896_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0896_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0896_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":896,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,0,3],[0,1,2],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8}],"canvas_size":[556,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0897","image_path":"images/combination3d_0897.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0897_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0897_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0897_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0897_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0897_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":897,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[603,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0898","image_path":"images/combination3d_0898.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0898_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0898_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0898_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0898_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0898_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":898,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0]],[[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[2,0,1],[2,0,2],[2,2,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[566,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0899","image_path":"images/combination3d_0899.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0899_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0899_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0899_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0899_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0899_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":899,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,2],[1,2,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,2]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,1,1],[2,2,1],[3,0,0],[3,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,2]]],"total_cube_count":14}],"canvas_size":[579,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0900","image_path":"images/combination3d_0900.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0900_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0900_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0900_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0900_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0900_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":900,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0],[0,4,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[605,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0901","image_path":"images/combination3d_0901.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0901_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0901_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0901_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_0901_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0901_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":901,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[0,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,3,1],[2,0,1]]],"total_cube_count":13}],"canvas_size":[584,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0902","image_path":"images/combination3d_0902.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0902_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0902_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0902_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_0902_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0902_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":902,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,2],[0,2,3],[0,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,2],[0,1,3],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[555,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0903","image_path":"images/combination3d_0903.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0903_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0903_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0903_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0903_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_0903_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":903,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":11}],"canvas_size":[586,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0904","image_path":"images/combination3d_0904.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0904_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0904_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0904_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0904_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0904_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":904,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,1],[1,1,3],[2,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,1],[2,2,1],[3,1,0],[3,1,1],[3,2,1]]],"total_cube_count":14}],"canvas_size":[594,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0905","image_path":"images/combination3d_0905.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0905_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0905_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0905_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0905_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0905_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":905,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[550,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0906","image_path":"images/combination3d_0906.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0906_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0906_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0906_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_0906_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0906_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":906,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,0,1],[3,1,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":10}],"canvas_size":[601,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0907","image_path":"images/combination3d_0907.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0907_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0907_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0907_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0907_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0907_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":907,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,3]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0]]],"total_cube_count":11}],"canvas_size":[554,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0908","image_path":"images/combination3d_0908.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0908_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0908_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0908_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_0908_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0908_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":908,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,3],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,2]]],"total_cube_count":11}],"canvas_size":[576,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0909","image_path":"images/combination3d_0909.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0909_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0909_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0909_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0909_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0909_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":909,"target_cube_count":11,"target_cubes":[[0,3,0],[0,3,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[1,2,1],[1,3,1],[1,3,2]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[607,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0910","image_path":"images/combination3d_0910.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0910_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0910_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0910_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0910_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_0910_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":910,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,1,1],[0,2,1],[0,3,1],[0,3,2],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,3,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[608,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0911","image_path":"images/combination3d_0911.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0911_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0911_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0911_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_0911_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0911_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":911,"target_cube_count":13,"target_cubes":[[0,1,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,2],[1,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":10}],"canvas_size":[617,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0912","image_path":"images/combination3d_0912.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0912_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0912_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0912_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0912_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0912_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":912,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,3,0],[3,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,3,0],[3,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,2],[0,2,2],[0,2,3],[0,3,0],[0,3,1],[0,3,2],[1,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[562,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0913","image_path":"images/combination3d_0913.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0913_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0913_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0913_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0913_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_0913_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":913,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,5,0],[2,0,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[1,1,0],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[557,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0914","image_path":"images/combination3d_0914.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0914_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0914_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0914_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0914_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0914_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":914,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":15}],"canvas_size":[572,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0915","image_path":"images/combination3d_0915.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0915_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0915_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0915_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0915_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0915_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":915,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,2]],[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,2],[0,1,3],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,2],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12}],"canvas_size":[574,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0916","image_path":"images/combination3d_0916.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0916_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0916_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0916_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0916_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0916_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":916,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9}],"canvas_size":[616,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0917","image_path":"images/combination3d_0917.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0917_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0917_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0917_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0917_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0917_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":917,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,1,0],[1,1,1],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,2,0],[1,3,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,3,0],[1,4,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":8}],"canvas_size":[608,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0918","image_path":"images/combination3d_0918.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0918_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0918_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0918_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0918_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0918_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":918,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,1],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[616,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0919","image_path":"images/combination3d_0919.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0919_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0919_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0919_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0919_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0919_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":919,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1],[2,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[590,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0920","image_path":"images/combination3d_0920.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0920_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0920_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0920_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0920_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0920_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":920,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,3],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":12}],"canvas_size":[594,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0921","image_path":"images/combination3d_0921.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0921_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0921_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0921_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,5","question_id":"combination3d_0921_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0921_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":921,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,1],[1,2,2],[1,3,1],[1,4,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,1],[3,0,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":15}],"canvas_size":[556,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0922","image_path":"images/combination3d_0922.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0922_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0922_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0922_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0922_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0922_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":922,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,2],[2,1,2],[2,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,2]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12}],"canvas_size":[611,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0923","image_path":"images/combination3d_0923.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0923_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0923_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0923_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0923_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0923_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":923,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[593,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0924","image_path":"images/combination3d_0924.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0924_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0924_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0924_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0924_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0924_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":924,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,2,0],[3,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,2,2],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,1,3],[0,2,3],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1]],[[0,1,1],[1,0,1],[1,1,1],[2,1,1],[2,1,2],[2,1,3],[3,1,0],[3,1,1],[3,2,1],[3,2,2]]],"total_cube_count":15}],"canvas_size":[561,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0925","image_path":"images/combination3d_0925.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0925_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0925_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0925_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0925_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0925_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":925,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,3,0],[2,3,1],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[603,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0926","image_path":"images/combination3d_0926.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0926_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0926_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0926_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0926_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0926_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":926,"target_cube_count":9,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[566,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0927","image_path":"images/combination3d_0927.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0927_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0927_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0927_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0927_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0927_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":927,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1],[2,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[589,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0928","image_path":"images/combination3d_0928.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0928_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0928_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0928_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0928_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0928_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":928,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[574,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0929","image_path":"images/combination3d_0929.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0929_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0929_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0929_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0929_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0929_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":929,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0]]],"total_cube_count":8}],"canvas_size":[616,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0930","image_path":"images/combination3d_0930.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0930_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0930_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0930_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0930_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0930_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":930,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,1],[1,3,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,2],[0,1,3],[0,1,4],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[604,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0931","image_path":"images/combination3d_0931.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0931_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0931_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0931_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0931_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0931_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":931,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[616,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0932","image_path":"images/combination3d_0932.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0932_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0932_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0932_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_0932_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0932_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":932,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[617,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0933","image_path":"images/combination3d_0933.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0933_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0933_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0933_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0933_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0933_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":933,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":8}],"canvas_size":[609,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0934","image_path":"images/combination3d_0934.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0934_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0934_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0934_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0934_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0934_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":934,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[608,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_0935","image_path":"images/combination3d_0935.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0935_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0935_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0935_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0935_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0935_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":935,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,1],[1,3,1],[1,3,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[569,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0936","image_path":"images/combination3d_0936.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0936_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0936_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0936_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_0936_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0936_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":936,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,2,0],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1],[2,1,1],[3,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,1],[2,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13}],"canvas_size":[618,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0937","image_path":"images/combination3d_0937.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0937_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0937_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0937_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0937_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_0937_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":937,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,1],[1,0,2],[1,1,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]]],"total_cube_count":10}],"canvas_size":[607,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0938","image_path":"images/combination3d_0938.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0938_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0938_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0938_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0938_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0938_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":938,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[562,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0939","image_path":"images/combination3d_0939.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0939_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0939_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0939_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0939_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_0939_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":939,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[595,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0940","image_path":"images/combination3d_0940.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0940_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0940_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0940_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0940_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_0940_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":940,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[595,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0941","image_path":"images/combination3d_0941.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0941_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0941_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0941_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0941_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0941_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":941,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1]],[[0,3,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1],[3,4,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1]],[[0,3,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[3,1,1],[3,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,1,3],[1,1,3],[1,1,4],[2,0,4],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]]],"total_cube_count":14}],"canvas_size":[600,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0942","image_path":"images/combination3d_0942.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0942_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0942_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0942_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_0942_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0942_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":942,"target_cube_count":14,"target_cubes":[[0,3,0],[0,3,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,4,0],[2,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,2],[2,0,2],[2,1,2],[3,0,2],[3,1,2]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,3,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":13}],"canvas_size":[619,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0943","image_path":"images/combination3d_0943.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0943_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0943_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0943_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_0943_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0943_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":943,"target_cube_count":12,"target_cubes":[[0,3,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,2,0],[3,3,0],[3,3,1],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]],[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,3,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12}],"canvas_size":[551,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0944","image_path":"images/combination3d_0944.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0944_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0944_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0944_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0944_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0944_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":944,"target_cube_count":12,"target_cubes":[[0,2,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,3,0],[3,2,0],[3,2,1],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[605,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0945","image_path":"images/combination3d_0945.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0945_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0945_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0945_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0945_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0945_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":945,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14}],"canvas_size":[554,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0946","image_path":"images/combination3d_0946.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0946_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0946_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0946_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0946_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0946_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":946,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,0,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,2,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10}],"canvas_size":[575,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0947","image_path":"images/combination3d_0947.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0947_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0947_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0947_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0947_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0947_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":947,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,1,1],[0,2,1],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14}],"canvas_size":[616,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0948","image_path":"images/combination3d_0948.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0948_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0948_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0948_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_0948_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0948_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":948,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[593,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0949","image_path":"images/combination3d_0949.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0949_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0949_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0949_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0949_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_0949_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":949,"target_cube_count":10,"target_cubes":[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[1,1,3]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,0,2],[1,1,1],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[577,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0950","image_path":"images/combination3d_0950.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0950_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0950_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0950_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0950_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0950_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":950,"target_cube_count":13,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,2,0],[3,2,1],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,3],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,1],[1,1,3],[1,2,0],[1,2,1],[1,3,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[572,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0951","image_path":"images/combination3d_0951.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0951_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0951_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0951_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0951_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0951_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":951,"target_cube_count":14,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8}],"canvas_size":[564,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0952","image_path":"images/combination3d_0952.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0952_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0952_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0952_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0952_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_0952_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":952,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,1,1]]],"total_cube_count":11}],"canvas_size":[550,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0953","image_path":"images/combination3d_0953.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0953_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0953_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0953_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0953_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0953_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":953,"target_cube_count":11,"target_cubes":[[0,1,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,1,1],[1,2,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":8}],"canvas_size":[572,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0954","image_path":"images/combination3d_0954.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0954_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0954_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0954_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_0954_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0954_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":954,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[1,0,1],[2,0,1],[3,0,1],[4,0,0],[4,0,1],[5,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0],[2,2,0]]],"total_cube_count":11}],"canvas_size":[602,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0955","image_path":"images/combination3d_0955.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0955_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0955_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0955_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0955_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0955_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":955,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[600,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_0956","image_path":"images/combination3d_0956.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0956_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0956_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0956_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_0956_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0956_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":956,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]]],"total_cube_count":15}],"canvas_size":[609,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0957","image_path":"images/combination3d_0957.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0957_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0957_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0957_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_0957_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0957_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":957,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,1,1],[2,1,1],[3,1,1]]],"total_cube_count":12}],"canvas_size":[591,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0958","image_path":"images/combination3d_0958.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0958_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0958_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0958_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0958_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0958_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":958,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8}],"canvas_size":[610,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0959","image_path":"images/combination3d_0959.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0959_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0959_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0959_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0959_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0959_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":959,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9}],"canvas_size":[599,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0960","image_path":"images/combination3d_0960.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0960_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0960_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0960_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0960_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_0960_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":960,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":8}],"canvas_size":[617,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0961","image_path":"images/combination3d_0961.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0961_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0961_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0961_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0961_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0961_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":961,"target_cube_count":8,"target_cubes":[[0,3,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[582,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0962","image_path":"images/combination3d_0962.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0962_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0962_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0962_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0962_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_0962_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":962,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[1,2,1],[1,2,2],[1,3,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2]],[[0,1,1],[0,2,1],[0,3,1],[0,3,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2]],[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1]],[[0,0,3],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":14}],"canvas_size":[619,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0963","image_path":"images/combination3d_0963.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0963_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0963_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0963_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0963_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0963_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":963,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":12}],"canvas_size":[614,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0964","image_path":"images/combination3d_0964.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0964_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0964_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0964_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0964_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0964_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":964,"target_cube_count":12,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,1,1],[2,1,2],[3,0,1],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[579,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0965","image_path":"images/combination3d_0965.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0965_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0965_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0965_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0965_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0965_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":965,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[554,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0966","image_path":"images/combination3d_0966.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0966_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0966_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0966_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0966_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0966_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":966,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,2,1],[2,2,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10}],"canvas_size":[617,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0967","image_path":"images/combination3d_0967.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0967_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0967_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0967_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0967_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0967_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":967,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1],[2,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[562,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0968","image_path":"images/combination3d_0968.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0968_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0968_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0968_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0968_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_0968_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":968,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[1,3,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,1],[2,1,1],[2,2,0],[2,2,1],[3,2,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[1,3,2],[2,3,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,1],[1,3,2],[2,1,1],[3,0,1],[3,1,1]]],"total_cube_count":13}],"canvas_size":[598,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0969","image_path":"images/combination3d_0969.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0969_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0969_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0969_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0969_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0969_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":969,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,1,1],[3,0,1],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[586,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0970","image_path":"images/combination3d_0970.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0970_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0970_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0970_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0970_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0970_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":970,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,1],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[583,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0971","image_path":"images/combination3d_0971.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0971_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0971_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0971_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_0971_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0971_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":971,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[565,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_0972","image_path":"images/combination3d_0972.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_0972_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0972_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0972_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0972_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_0972_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":972,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8}],"canvas_size":[569,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0973","image_path":"images/combination3d_0973.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0973_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0973_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0973_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0973_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0973_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":973,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,1],[0,4,1],[0,4,2],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[1,4,1],[1,4,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,4],[1,1,4]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[592,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0974","image_path":"images/combination3d_0974.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0974_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0974_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0974_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0974_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0974_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":974,"target_cube_count":12,"target_cubes":[[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,1,2],[1,1,3],[1,2,2],[1,3,2],[2,1,2],[2,2,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,1],[2,0,2],[3,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[1,2,2],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[613,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0975","image_path":"images/combination3d_0975.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0975_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0975_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0975_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0975_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_0975_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":975,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,0,0],[1,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":13}],"canvas_size":[592,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_0976","image_path":"images/combination3d_0976.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0976_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0976_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0976_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0976_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_0976_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":976,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,1],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[556,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0977","image_path":"images/combination3d_0977.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0977_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0977_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0977_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_0977_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0977_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":977,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[1,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":8}],"canvas_size":[569,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0978","image_path":"images/combination3d_0978.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0978_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0978_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0978_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0978_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0978_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":978,"target_cube_count":8,"target_cubes":[[0,3,0],[0,3,1],[1,2,0],[1,3,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,2,0],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[4,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[609,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0979","image_path":"images/combination3d_0979.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0979_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0979_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0979_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0979_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0979_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":979,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,3]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":9}],"canvas_size":[604,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0980","image_path":"images/combination3d_0980.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0980_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0980_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0980_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0980_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_0980_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":980,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,1,1]]],"total_cube_count":10}],"canvas_size":[578,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0981","image_path":"images/combination3d_0981.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0981_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0981_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0981_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_0981_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0981_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":981,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,0,0],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[1,0,1],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14}],"canvas_size":[614,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_0982","image_path":"images/combination3d_0982.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0982_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0982_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0982_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0982_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_0982_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":982,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":12}],"canvas_size":[617,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0983","image_path":"images/combination3d_0983.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0983_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0983_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0983_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0983_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_0983_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":983,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9}],"canvas_size":[562,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0984","image_path":"images/combination3d_0984.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0984_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0984_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0984_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0984_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0984_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":984,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[592,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_0985","image_path":"images/combination3d_0985.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0985_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0985_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_0985_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0985_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_0985_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":985,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[565,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0986","image_path":"images/combination3d_0986.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0986_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0986_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0986_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_0986_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0986_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":986,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[2,0,2],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[3,0,0],[3,0,1],[3,1,1],[4,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":13}],"canvas_size":[618,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0987","image_path":"images/combination3d_0987.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0987_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0987_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0987_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0987_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0987_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":987,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[3,0,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[588,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0988","image_path":"images/combination3d_0988.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0988_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0988_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0988_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_0988_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_0988_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":988,"target_cube_count":8,"target_cubes":[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[560,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_0989","image_path":"images/combination3d_0989.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0989_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0989_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0989_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_0989_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0989_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":989,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,1,2],[1,2,1],[1,2,2],[2,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,1],[1,2,2],[1,2,3],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[614,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0990","image_path":"images/combination3d_0990.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0990_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0990_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0990_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_0990_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0990_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":990,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":14}],"canvas_size":[568,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_0991","image_path":"images/combination3d_0991.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_0991_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0991_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0991_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0991_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_0991_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":991,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2],[2,3,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[2,2,0],[2,2,1],[3,2,0],[3,2,1],[3,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,2],[0,3,2],[1,1,2],[1,2,2],[1,3,2],[2,3,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,2,0],[2,2,1],[3,2,0],[3,2,1],[3,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[575,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0992","image_path":"images/combination3d_0992.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0992_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0992_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0992_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_0992_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0992_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":992,"target_cube_count":14,"target_cubes":[[0,2,0],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,4,0],[3,2,0],[3,2,1],[4,2,0],[4,2,1],[4,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,1],[1,2,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0]]],"total_cube_count":9}],"canvas_size":[557,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_0993","image_path":"images/combination3d_0993.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_0993_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0993_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0993_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0993_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_0993_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":993,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[566,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_0994","image_path":"images/combination3d_0994.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0994_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0994_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0994_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_0994_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_0994_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":994,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":10}],"canvas_size":[573,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0995","image_path":"images/combination3d_0995.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0995_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0995_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_0995_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_0995_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_0995_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":995,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9}],"canvas_size":[606,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_0996","image_path":"images/combination3d_0996.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_0996_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_0996_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0996_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0996_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_0996_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":996,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[609,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_0997","image_path":"images/combination3d_0997.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_0997_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_0997_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_0997_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_0997_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0997_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":997,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,2,0],[3,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[571,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_0998","image_path":"images/combination3d_0998.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_0998_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_0998_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0998_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_0998_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_0998_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":998,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,3],[1,1,2],[1,2,1],[1,2,2],[1,2,3],[2,0,2],[2,1,2],[2,2,1],[2,2,2],[3,1,0],[3,2,0],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,1],[2,1,2],[2,1,3],[2,2,1],[2,2,2],[3,2,1],[3,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,2,0],[3,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,1],[1,0,1],[1,1,2],[1,2,2],[1,2,3]]],"total_cube_count":14}],"canvas_size":[560,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_0999","image_path":"images/combination3d_0999.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_0999_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_0999_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_0999_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_0999_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_0999_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":999,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,0,1],[3,1,0],[4,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,1,0]],[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,1,5],[1,0,1],[1,0,2],[1,0,3],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,1],[1,0,2],[1,0,3],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[604,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1000","image_path":"images/combination3d_1000.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1000_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1000_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1000_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1000_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1000_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1000,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,1],[2,0,0],[2,1,0]],[[0,1,2],[1,0,2],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[3,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,0,3]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[4,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[557,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1001","image_path":"images/combination3d_1001.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1001_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1001_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1001_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1001_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1001_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1001,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12}],"canvas_size":[616,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1002","image_path":"images/combination3d_1002.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1002_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1002_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1002_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_1002_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1002_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1002,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":10}],"canvas_size":[613,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1003","image_path":"images/combination3d_1003.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1003_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1003_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1003_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1003_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1003_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1003,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0],[4,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[4,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[4,0,0]]],"total_cube_count":13}],"canvas_size":[603,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1004","image_path":"images/combination3d_1004.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1004_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1004_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1004_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1004_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1004_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1004,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[3,0,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,0,2],[3,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[611,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1005","image_path":"images/combination3d_1005.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1005_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1005_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1005_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1005_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1005_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1005,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,2,1],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[594,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1006","image_path":"images/combination3d_1006.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1006_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1006_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1006_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1006_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1006_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1006,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[3,0,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,2],[0,1,3],[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,3]]],"total_cube_count":14}],"canvas_size":[554,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1007","image_path":"images/combination3d_1007.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1007_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1007_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1007_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1007_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1007_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1007,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":10}],"canvas_size":[616,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1008","image_path":"images/combination3d_1008.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1008_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1008_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1008_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1008_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1008_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1008,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,1],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[573,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1009","image_path":"images/combination3d_1009.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1009_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1009_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1009_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1009_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1009_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1009,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[581,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1010","image_path":"images/combination3d_1010.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1010_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1010_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1010_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1010_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1010_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1010,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[596,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1011","image_path":"images/combination3d_1011.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1011_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1011_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1011_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1011_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1011_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1011,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,0,2],[1,1,1],[2,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":9}],"canvas_size":[593,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1012","image_path":"images/combination3d_1012.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1012_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1012_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1012_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1012_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1012_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1012,"target_cube_count":9,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0],[4,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[612,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1013","image_path":"images/combination3d_1013.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1013_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1013_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1013_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1013_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1013_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1013,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,3],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[615,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1014","image_path":"images/combination3d_1014.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1014_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1014_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1014_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1014_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1014_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1014,"target_cube_count":9,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[563,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1015","image_path":"images/combination3d_1015.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1015_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1015_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1015_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1015_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1015_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1015,"target_cube_count":10,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[0,4,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[596,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1016","image_path":"images/combination3d_1016.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1016_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1016_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1016_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1016_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1016_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1016,"target_cube_count":11,"target_cubes":[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":13}],"canvas_size":[611,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1017","image_path":"images/combination3d_1017.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1017_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1017_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1017_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1017_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1017_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1017,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,2,0],[2,2,1],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[600,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1018","image_path":"images/combination3d_1018.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1018_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1018_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1018_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1018_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1018_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1018,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[554,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1019","image_path":"images/combination3d_1019.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1019_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1019_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1019_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1019_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1019_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1019,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[1,2,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11}],"canvas_size":[564,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1020","image_path":"images/combination3d_1020.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1020_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1020_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1020_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1020_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1020_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1020,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1],[3,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10}],"canvas_size":[617,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1021","image_path":"images/combination3d_1021.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1021_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1021_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1021_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1021_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1021_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1021,"target_cube_count":9,"target_cubes":[[0,2,0],[0,3,0],[0,4,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,2,0],[2,0,1],[2,1,1],[2,2,0],[2,2,1],[3,1,1],[3,2,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,3,0]]],"total_cube_count":12}],"canvas_size":[566,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1022","image_path":"images/combination3d_1022.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1022_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1022_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1022_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1022_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1022_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1022,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,2],[1,1,2]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,2,0],[1,2,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,2,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12}],"canvas_size":[612,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1023","image_path":"images/combination3d_1023.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1023_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1023_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1023_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1023_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1023_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1023,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,2,0],[1,2,1],[1,4,0],[1,4,1],[1,4,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,0,3],[1,1,2],[1,1,3]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14}],"canvas_size":[552,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1024","image_path":"images/combination3d_1024.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1024_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1024_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1024_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1024_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1024_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1024,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[576,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1025","image_path":"images/combination3d_1025.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1025_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1025_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1025_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1025_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1025_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1025,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[553,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1026","image_path":"images/combination3d_1026.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1026_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1026_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1026_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1026_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1026_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1026,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[552,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1027","image_path":"images/combination3d_1027.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1027_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1027_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1027_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_1027_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1027_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1027,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,3,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[2,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":11}],"canvas_size":[609,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1028","image_path":"images/combination3d_1028.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1028_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1028_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1028_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1028_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1028_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1028,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[0,3,2],[1,3,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]]],"total_cube_count":13}],"canvas_size":[589,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1029","image_path":"images/combination3d_1029.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1029_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1029_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1029_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1029_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1029_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1029,"target_cube_count":12,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":14}],"canvas_size":[557,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1030","image_path":"images/combination3d_1030.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1030_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1030_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1030_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1030_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1030_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1030,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[3,1,0],[3,1,1],[3,1,2],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,1],[0,1,1],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0]]],"total_cube_count":9}],"canvas_size":[620,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1031","image_path":"images/combination3d_1031.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1031_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1031_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1031_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1031_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1031_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1031,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[599,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1032","image_path":"images/combination3d_1032.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1032_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1032_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1032_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1032_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1032_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1032,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[576,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1033","image_path":"images/combination3d_1033.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1033_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1033_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1033_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1033_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1033_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1033,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[554,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1034","image_path":"images/combination3d_1034.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1034_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1034_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1034_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_1034_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1034_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1034,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":10}],"canvas_size":[606,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1035","image_path":"images/combination3d_1035.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1035_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1035_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1035_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1035_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1035_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1035,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[2,0,2]],[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]]],"total_cube_count":13}],"canvas_size":[603,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1036","image_path":"images/combination3d_1036.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1036_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1036_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1036_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1036_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1036_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1036,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,0,2],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,1,0],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14}],"canvas_size":[560,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1037","image_path":"images/combination3d_1037.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1037_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1037_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1037_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1037_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1037_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1037,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[2,1,3]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[564,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1038","image_path":"images/combination3d_1038.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1038_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1038_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1038_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1038_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1038_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1038,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,0,2],[1,1,1],[2,0,2],[2,0,3],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,2]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[573,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1039","image_path":"images/combination3d_1039.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1039_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1039_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1039_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1039_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_1039_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1039,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,3],[1,1,1],[1,1,2],[1,1,3],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[1,3,2],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[589,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1040","image_path":"images/combination3d_1040.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1040_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1040_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1040_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1040_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1040_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1040,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11}],"canvas_size":[606,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1041","image_path":"images/combination3d_1041.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1041_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1041_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1041_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1041_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1041_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1041,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[4,0,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[581,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1042","image_path":"images/combination3d_1042.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1042_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1042_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1042_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_1042_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1042_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1042,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[596,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1043","image_path":"images/combination3d_1043.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1043_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1043_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1043_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1043_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1043_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1043,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,1],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[578,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1044","image_path":"images/combination3d_1044.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1044_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1044_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1044_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1044_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1044_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1044,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,1],[2,1,2]],[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]]],"total_cube_count":13}],"canvas_size":[554,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1045","image_path":"images/combination3d_1045.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1045_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1045_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1045_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1045_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1045_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1045,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,1,1],[3,2,0],[3,3,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[1,2,1],[1,3,1],[1,3,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,2],[2,0,0],[2,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":15}],"canvas_size":[609,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1046","image_path":"images/combination3d_1046.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1046_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1046_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1046_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1046_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1046_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1046,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0],[3,1,1],[3,1,2],[3,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,2,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[560,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1047","image_path":"images/combination3d_1047.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1047_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1047_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1047_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1047_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1047_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1047,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,0,2],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[584,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1048","image_path":"images/combination3d_1048.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1048_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1048_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1048_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1048_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_1048_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1048,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[1,0,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]]],"total_cube_count":8}],"canvas_size":[607,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1049","image_path":"images/combination3d_1049.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1049_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1049_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1049_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_1049_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1049_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1049,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[591,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1050","image_path":"images/combination3d_1050.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1050_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1050_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1050_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1050_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1050_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1050,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8}],"canvas_size":[556,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1051","image_path":"images/combination3d_1051.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1051_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1051_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1051_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1051_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1051_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1051,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14}],"canvas_size":[569,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1052","image_path":"images/combination3d_1052.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1052_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1052_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1052_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1052_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1052_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1052,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,2,0],[0,2,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,2],[2,1,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,2,1],[0,2,2],[1,2,1],[2,0,0],[2,0,1],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14}],"canvas_size":[594,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1053","image_path":"images/combination3d_1053.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1053_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1053_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1053_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1053_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1053_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1053,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,3,0],[3,3,0],[4,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,2],[3,1,2],[4,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,1,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,2],[2,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[565,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1054","image_path":"images/combination3d_1054.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1054_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1054_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1054_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1054_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1054_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1054,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[561,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1055","image_path":"images/combination3d_1055.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1055_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1055_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1055_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1055_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1055_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1055,"target_cube_count":10,"target_cubes":[[0,0,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,2,2],[0,3,2],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,2],[2,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,2,3],[2,3,2],[2,3,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[564,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1056","image_path":"images/combination3d_1056.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1056_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1056_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1056_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1056_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1056_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1056,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,2,1],[1,3,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":11}],"canvas_size":[620,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1057","image_path":"images/combination3d_1057.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1057_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1057_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1057_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1057_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1057_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1057,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[3,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[588,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1058","image_path":"images/combination3d_1058.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1058_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1058_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1058_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1058_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1058_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1058,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[0,4,0],[0,4,1],[1,3,0],[1,4,0],[2,3,0],[2,4,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[555,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1059","image_path":"images/combination3d_1059.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1059_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1059_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1059_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1059_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_1059_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1059,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":8}],"canvas_size":[581,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1060","image_path":"images/combination3d_1060.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1060_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1060_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1060_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_1060_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1060_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1060,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10}],"canvas_size":[618,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1061","image_path":"images/combination3d_1061.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1061_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1061_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1061_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_1061_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1061_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1061,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[564,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1062","image_path":"images/combination3d_1062.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1062_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1062_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1062_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1062_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1062_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1062,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1]],[[0,1,0],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,1,2],[2,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]],[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[2,2,1]]],"total_cube_count":14}],"canvas_size":[575,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1063","image_path":"images/combination3d_1063.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1063_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1063_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1063_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_1063_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1063_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1063,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[581,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1064","image_path":"images/combination3d_1064.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1064_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1064_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1064_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1064_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1064_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1064,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]]],"total_cube_count":15}],"canvas_size":[565,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1065","image_path":"images/combination3d_1065.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1065_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1065_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1065_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1065_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1065_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1065,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,2,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,2],[1,0,1],[1,1,2],[2,0,1],[2,1,1],[2,1,2],[2,2,2],[2,3,0],[2,3,1],[2,3,2],[2,4,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[607,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1066","image_path":"images/combination3d_1066.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1066_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1066_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1066_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1066_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1066_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1066,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,0,1],[1,2,0],[1,2,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,2],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,2],[1,2,2],[1,3,2]]],"total_cube_count":11}],"canvas_size":[551,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1067","image_path":"images/combination3d_1067.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1067_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1067_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1067_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1067_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1067_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1067,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[603,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1068","image_path":"images/combination3d_1068.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1068_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1068_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1068_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1068_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1068_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1068,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9}],"canvas_size":[595,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1069","image_path":"images/combination3d_1069.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1069_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1069_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1069_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1069_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1069_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1069,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8}],"canvas_size":[594,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1070","image_path":"images/combination3d_1070.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1070_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1070_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1070_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1070_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1070_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1070,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,1],[1,1,2],[1,2,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,1],[1,2,1],[1,3,1],[1,3,2],[2,2,0],[2,2,1],[3,0,1],[3,1,1],[3,2,0],[3,2,1],[4,2,1],[4,2,2]]],"total_cube_count":14}],"canvas_size":[564,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1071","image_path":"images/combination3d_1071.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1071_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1071_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1071_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1071_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1071_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1071,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,1],[2,1,0],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[613,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1072","image_path":"images/combination3d_1072.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1072_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1072_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1072_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1072_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1072_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1072,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8}],"canvas_size":[591,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1073","image_path":"images/combination3d_1073.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1073_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1073_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1073_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1073_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1073_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1073,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[598,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1074","image_path":"images/combination3d_1074.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1074_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1074_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1074_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_1074_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1074_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1074,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10}],"canvas_size":[605,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1075","image_path":"images/combination3d_1075.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1075_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1075_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1075_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1075_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1075_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1075,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2],[0,2,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[595,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1076","image_path":"images/combination3d_1076.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1076_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1076_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1076_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1076_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1076_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1076,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[556,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1077","image_path":"images/combination3d_1077.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1077_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1077_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1077_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1077_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1077_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1077,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":11}],"canvas_size":[562,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1078","image_path":"images/combination3d_1078.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1078_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1078_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1078_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_1078_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1078_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1078,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":11}],"canvas_size":[618,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1079","image_path":"images/combination3d_1079.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1079_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1079_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1079_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_1079_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1079_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1079,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[1,1,0],[1,1,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]]],"total_cube_count":12}],"canvas_size":[613,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1080","image_path":"images/combination3d_1080.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1080_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1080_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1080_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1080_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1080_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1080,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[610,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1081","image_path":"images/combination3d_1081.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1081_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1081_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1081_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1081_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1081_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1081,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,2,1],[1,3,1],[2,3,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2]]],"total_cube_count":15}],"canvas_size":[574,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1082","image_path":"images/combination3d_1082.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1082_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1082_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1082_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1082_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1082_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1082,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[577,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1083","image_path":"images/combination3d_1083.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1083_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1083_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1083_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1083_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1083_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1083,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[555,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1084","image_path":"images/combination3d_1084.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1084_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1084_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1084_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1084_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1084_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1084,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[2,0,0]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,2],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[619,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1085","image_path":"images/combination3d_1085.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1085_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1085_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1085_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1085_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_1085_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1085,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,4,0],[3,0,0],[3,1,0],[4,1,0],[4,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[3,0,0],[3,1,0],[4,1,0],[4,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,4,0],[0,4,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[0,3,0],[0,3,1],[0,4,1],[1,2,2],[1,4,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[598,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1086","image_path":"images/combination3d_1086.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1086_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1086_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1086_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1086_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1086_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1086,"target_cube_count":14,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0],[3,3,1],[4,1,0],[4,2,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":15}],"canvas_size":[575,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1087","image_path":"images/combination3d_1087.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1087_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1087_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1087_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1087_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1087_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1087,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0],[3,3,1],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[618,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1088","image_path":"images/combination3d_1088.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1088_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1088_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1088_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1088_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1088_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1088,"target_cube_count":12,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[2,3,1],[2,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,2,2],[0,3,0],[0,3,1],[0,3,2],[1,3,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1]]],"total_cube_count":12}],"canvas_size":[590,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1089","image_path":"images/combination3d_1089.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1089_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1089_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1089_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1089_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1089_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1089,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[4,1,0],[5,1,0],[5,1,1],[5,1,2],[5,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,2],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[607,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1090","image_path":"images/combination3d_1090.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1090_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1090_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1090_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1090_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1090_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1090,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,3],[0,1,4],[0,1,5],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,2],[1,1,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[2,0,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,0,0],[1,0,1],[1,3,0],[1,4,0],[1,5,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,0,1],[1,3,0],[1,4,0],[1,4,1],[1,5,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[596,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1091","image_path":"images/combination3d_1091.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1091_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1091_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1091_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1091_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1091_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1091,"target_cube_count":14,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,3,0],[1,4,0],[1,5,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[614,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1092","image_path":"images/combination3d_1092.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1092_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1092_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1092_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1092_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1092_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1092,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[593,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1093","image_path":"images/combination3d_1093.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1093_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1093_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1093_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1093_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1093_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1093,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,1],[2,1,1],[2,2,1],[3,0,1],[3,1,1],[3,2,0],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[619,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1094","image_path":"images/combination3d_1094.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1094_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1094_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1094_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1094_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1094_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1094,"target_cube_count":13,"target_cubes":[[0,0,0],[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,4,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[577,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1095","image_path":"images/combination3d_1095.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1095_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1095_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1095_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_1095_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1095_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1095,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[0,3,0],[0,3,1],[0,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,1],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[604,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1096","image_path":"images/combination3d_1096.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1096_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1096_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1096_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1096_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1096_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1096,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[617,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1097","image_path":"images/combination3d_1097.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1097_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1097_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1097_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1097_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1097_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1097,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,3,1],[1,0,2],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[572,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1098","image_path":"images/combination3d_1098.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1098_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1098_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1098_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1098_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1098_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1098,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[3,0,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[601,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1099","image_path":"images/combination3d_1099.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1099_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1099_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1099_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1099_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1099_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1099,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[553,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1100","image_path":"images/combination3d_1100.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1100_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1100_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1100_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1100_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1100_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1100,"target_cube_count":9,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,0,2],[2,1,1],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12}],"canvas_size":[595,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1101","image_path":"images/combination3d_1101.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1101_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1101_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1101_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1101_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1101_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1101,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[0,4,1]],[[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":13}],"canvas_size":[596,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1102","image_path":"images/combination3d_1102.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1102_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1102_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1102_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1102_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1102_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1102,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12}],"canvas_size":[601,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1103","image_path":"images/combination3d_1103.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1103_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1103_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1103_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1103_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1103_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1103,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[3,2,0],[4,0,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[582,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1104","image_path":"images/combination3d_1104.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1104_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1104_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1104_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1104_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_1104_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1104,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,2],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[552,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1105","image_path":"images/combination3d_1105.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1105_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1105_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1105_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1105_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1105_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1105,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10}],"canvas_size":[608,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1106","image_path":"images/combination3d_1106.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1106_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1106_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1106_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1106_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_1106_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1106,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[567,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1107","image_path":"images/combination3d_1107.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1107_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1107_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1107_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1107_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1107_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1107,"target_cube_count":10,"target_cubes":[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[4,1,0],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,1],[0,1,1],[1,1,1],[2,1,1],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0],[3,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[581,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1108","image_path":"images/combination3d_1108.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1108_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1108_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1108_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1108_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1108_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1108,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[3,2,0]]],"total_cube_count":11}],"canvas_size":[599,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1109","image_path":"images/combination3d_1109.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1109_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1109_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1109_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1109_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1109_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1109,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[0,2,1],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[0,2,1],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,0,3],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":13}],"canvas_size":[611,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1110","image_path":"images/combination3d_1110.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1110_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1110_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1110_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1110_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1110_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1110,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[577,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1111","image_path":"images/combination3d_1111.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1111_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1111_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1111_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_1111_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1111_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1111,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,3,0],[1,4,0],[1,5,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,3,0],[0,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[586,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1112","image_path":"images/combination3d_1112.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1112_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1112_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1112_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_1112_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1112_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1112,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1]]],"total_cube_count":9}],"canvas_size":[553,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1113","image_path":"images/combination3d_1113.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1113_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1113_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1113_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,5","question_id":"combination3d_1113_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1113_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1113,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,3,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,2,0],[1,3,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,2],[1,0,3]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,1,0],[1,1,1]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[617,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1114","image_path":"images/combination3d_1114.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1114_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1114_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1114_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1114_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1114_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1114,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,2,0],[1,3,0],[1,4,0],[1,5,0],[1,5,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,1,1]]],"total_cube_count":9}],"canvas_size":[584,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1115","image_path":"images/combination3d_1115.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1115_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1115_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1115_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1115_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1115_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1115,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":13}],"canvas_size":[605,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1116","image_path":"images/combination3d_1116.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1116_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1116_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1116_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1116_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1116_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1116,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":8}],"canvas_size":[608,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1117","image_path":"images/combination3d_1117.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1117_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1117_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1117_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1117_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1117_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1117,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[1,3,2],[2,3,0],[2,3,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[2,1,1],[3,1,1]],[[0,2,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":13}],"canvas_size":[579,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1118","image_path":"images/combination3d_1118.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1118_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1118_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1118_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1118_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1118_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1118,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,2,1]],[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,3]]],"total_cube_count":12}],"canvas_size":[557,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1119","image_path":"images/combination3d_1119.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1119_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1119_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1119_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1119_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1119_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1119,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[565,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1120","image_path":"images/combination3d_1120.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1120_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1120_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1120_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1120_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1120_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1120,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":12}],"canvas_size":[581,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1121","image_path":"images/combination3d_1121.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1121_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1121_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1121_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1121_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1121_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1121,"target_cube_count":12,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[1,1,2],[1,2,0],[1,2,1],[2,1,2]]],"total_cube_count":12}],"canvas_size":[609,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1122","image_path":"images/combination3d_1122.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1122_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1122_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1122_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1122_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_1122_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1122,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0]],[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[585,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1123","image_path":"images/combination3d_1123.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1123_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1123_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1123_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1123_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1123_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1123,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0],[1,3,0],[1,4,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,3],[0,1,4],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0],[1,3,0],[1,4,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[554,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1124","image_path":"images/combination3d_1124.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1124_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1124_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1124_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1124_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1124_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1124,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0],[0,5,0],[0,5,1],[1,3,0],[1,4,0],[1,5,0],[2,5,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10}],"canvas_size":[569,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1125","image_path":"images/combination3d_1125.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1125_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1125_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1125_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1125_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1125_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1125,"target_cube_count":10,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":9}],"canvas_size":[584,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1126","image_path":"images/combination3d_1126.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1126_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1126_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1126_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1126_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,6","question_id":"combination3d_1126_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1126,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10}],"canvas_size":[613,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1127","image_path":"images/combination3d_1127.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1127_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1127_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1127_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1127_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1127_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1127,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[559,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1128","image_path":"images/combination3d_1128.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1128_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1128_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1128_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1128_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1128_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1128,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,2,0],[2,2,0],[2,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,1],[3,0,1],[3,1,1],[4,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,2],[1,2,0],[2,2,0],[2,2,1]]],"total_cube_count":15}],"canvas_size":[612,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1129","image_path":"images/combination3d_1129.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1129_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1129_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1129_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1129_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1129_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1129,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,2,0],[1,2,1],[1,2,2],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,2],[0,3,2],[1,1,0],[1,1,1],[1,2,1],[1,2,2],[1,2,3],[1,2,4],[1,3,4],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":14}],"canvas_size":[619,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1130","image_path":"images/combination3d_1130.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1130_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1130_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1130_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1130_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1130_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1130,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12}],"canvas_size":[550,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1131","image_path":"images/combination3d_1131.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1131_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1131_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1131_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_1131_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1131_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1131,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,2],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,2,1],[2,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":14}],"canvas_size":[619,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1132","image_path":"images/combination3d_1132.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1132_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1132_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1132_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_1132_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1132_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1132,"target_cube_count":14,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,2,1],[1,2,2],[1,3,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[602,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1133","image_path":"images/combination3d_1133.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1133_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1133_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1133_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_1133_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1133_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1133,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,3],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,3],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,1],[0,2,2],[0,3,1],[0,3,2],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[555,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1134","image_path":"images/combination3d_1134.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1134_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1134_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1134_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1134_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1134_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1134,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[619,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1135","image_path":"images/combination3d_1135.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1135_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1135_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1135_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1135_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1135_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1135,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[554,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1136","image_path":"images/combination3d_1136.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1136_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1136_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1136_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1136_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1136_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1136,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2]]],"total_cube_count":9}],"canvas_size":[601,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1137","image_path":"images/combination3d_1137.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1137_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1137_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1137_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1137_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1137_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1137,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,1,0],[3,1,1],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,4,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,3,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,3],[1,0,0],[1,0,3]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1],[2,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1]]],"total_cube_count":12}],"canvas_size":[586,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1138","image_path":"images/combination3d_1138.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1138_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1138_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1138_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1138_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1138_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1138,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,4,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,3]]],"total_cube_count":9}],"canvas_size":[564,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1139","image_path":"images/combination3d_1139.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1139_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1139_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1139_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1139_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1139_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1139,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,2],[2,0,3],[3,0,3]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[596,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1140","image_path":"images/combination3d_1140.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1140_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1140_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1140_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1140_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1140_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1140,"target_cube_count":9,"target_cubes":[[0,2,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[601,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1141","image_path":"images/combination3d_1141.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1141_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1141_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1141_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1141_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1141_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1141,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[558,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1142","image_path":"images/combination3d_1142.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1142_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1142_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1142_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1142_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1142_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1142,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[2,2,0],[2,2,1],[2,2,2],[3,0,2],[3,1,2],[3,2,1],[3,2,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[574,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1143","image_path":"images/combination3d_1143.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1143_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1143_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1143_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1143_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1143_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1143,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,1,0],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[3,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[615,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1144","image_path":"images/combination3d_1144.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1144_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1144_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1144_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1144_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1144_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1144,"target_cube_count":11,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,4,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10}],"canvas_size":[575,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1145","image_path":"images/combination3d_1145.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1145_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1145_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1145_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1145_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1145_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1145,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[3,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1]]],"total_cube_count":12}],"canvas_size":[606,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1146","image_path":"images/combination3d_1146.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1146_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1146_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1146_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1146_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1146_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1146,"target_cube_count":11,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,0,0],[2,2,0],[2,2,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,1],[1,3,1],[2,0,2],[2,1,2],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[2,3,1],[2,3,2],[3,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[568,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1147","image_path":"images/combination3d_1147.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1147_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1147_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1147_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1147_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1147_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1147,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[2,2,0],[3,2,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[606,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1148","image_path":"images/combination3d_1148.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1148_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1148_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1148_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1148_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1148_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1148,"target_cube_count":13,"target_cubes":[[0,2,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,3,0],[3,3,1],[3,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[0,2,1],[1,0,2],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[579,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1149","image_path":"images/combination3d_1149.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1149_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1149_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1149_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1149_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1149_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1149,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,2,1],[1,3,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[567,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1150","image_path":"images/combination3d_1150.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1150_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1150_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1150_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1150_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1150_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1150,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,1],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,2,0],[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":13}],"canvas_size":[567,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1151","image_path":"images/combination3d_1151.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1151_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1151_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1151_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1151_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1151_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1151,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,0,2],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[561,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1152","image_path":"images/combination3d_1152.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1152_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1152_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1152_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1152_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1152_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1152,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,2],[1,0,0],[1,1,0],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[558,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1153","image_path":"images/combination3d_1153.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1153_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1153_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1153_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1153_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1153_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1153,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[3,0,0],[3,0,1],[3,1,0],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":8}],"canvas_size":[618,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1154","image_path":"images/combination3d_1154.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1154_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1154_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1154_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1154_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,5","question_id":"combination3d_1154_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1154,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,1]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[574,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1155","image_path":"images/combination3d_1155.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1155_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1155_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1155_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1155_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1155_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1155,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,3,1],[0,3,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":10}],"canvas_size":[563,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1156","image_path":"images/combination3d_1156.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1156_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1156_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1156_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1156_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1156_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1156,"target_cube_count":10,"target_cubes":[[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,2,0],[0,2,1],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":15}],"canvas_size":[599,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1157","image_path":"images/combination3d_1157.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1157_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1157_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1157_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1157_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1157_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1157,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,1,1],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[586,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1158","image_path":"images/combination3d_1158.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1158_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1158_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1158_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1158_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1158_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1158,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,2]],[[0,0,1],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]]],"total_cube_count":14}],"canvas_size":[574,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1159","image_path":"images/combination3d_1159.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1159_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1159_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1159_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_1159_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1159_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1159,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[606,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1160","image_path":"images/combination3d_1160.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1160_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1160_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1160_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1160_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1160_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1160,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8}],"canvas_size":[594,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1161","image_path":"images/combination3d_1161.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1161_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1161_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1161_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_1161_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1161_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1161,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":9}],"canvas_size":[610,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1162","image_path":"images/combination3d_1162.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1162_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1162_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1162_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_1162_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1162_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1162,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[557,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1163","image_path":"images/combination3d_1163.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1163_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1163_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1163_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1163_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1163_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1163,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,1,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,4,1],[1,0,0],[1,1,0],[1,2,0],[1,2,2],[1,3,0],[1,3,2],[1,4,0],[1,4,1],[1,4,2],[2,3,2],[2,4,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,2],[0,1,1],[0,1,2],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,2,3],[2,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":14}],"canvas_size":[571,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1164","image_path":"images/combination3d_1164.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1164_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1164_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1164_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1164_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1164_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1164,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,2,1]],[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,1,2],[1,2,2],[1,3,2]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":15}],"canvas_size":[568,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1165","image_path":"images/combination3d_1165.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1165_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1165_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1165_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1165_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1165_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1165,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[3,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[1,1,2],[1,1,3],[1,2,1],[2,1,3]]],"total_cube_count":12}],"canvas_size":[557,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1166","image_path":"images/combination3d_1166.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1166_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1166_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1166_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1166_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1166_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1166,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[4,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0]],[[0,2,3],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,2,3],[2,0,1],[2,2,0],[2,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,2],[1,0,3],[1,0,4]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,2],[1,0,3],[1,0,4],[1,0,5]]],"total_cube_count":15}],"canvas_size":[578,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1167","image_path":"images/combination3d_1167.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1167_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1167_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1167_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1167_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1167_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1167,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,0,1],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,3,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,3,0],[3,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[3,0,0]]],"total_cube_count":13}],"canvas_size":[562,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1168","image_path":"images/combination3d_1168.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1168_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1168_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1168_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1168_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1168_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1168,"target_cube_count":13,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[3,3,0],[4,0,0],[5,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8}],"canvas_size":[552,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1169","image_path":"images/combination3d_1169.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1169_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1169_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1169_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1169_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1169_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1169,"target_cube_count":8,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[555,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1170","image_path":"images/combination3d_1170.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1170_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1170_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1170_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1170_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_1170_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1170,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1]]],"total_cube_count":9}],"canvas_size":[600,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1171","image_path":"images/combination3d_1171.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1171_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1171_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1171_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1171_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1171_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1171,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,2,1],[1,2,0],[1,2,1],[2,0,1],[2,1,1],[2,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,2,1],[2,2,2],[3,1,1],[3,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":12}],"canvas_size":[620,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1172","image_path":"images/combination3d_1172.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1172_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1172_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1172_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1172_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1172_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1172,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[3,1,0],[4,0,0],[4,1,0],[5,1,0],[5,1,1],[5,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,1],[2,0,1],[3,0,0],[3,0,1],[3,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,0,1]]],"total_cube_count":9}],"canvas_size":[603,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1173","image_path":"images/combination3d_1173.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1173_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1173_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1173_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1173_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1173_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1173,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1]]],"total_cube_count":10}],"canvas_size":[578,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1174","image_path":"images/combination3d_1174.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1174_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1174_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1174_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1174_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1174_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1174,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0]],[[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[605,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1175","image_path":"images/combination3d_1175.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1175_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1175_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1175_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1175_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1175_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1175,"target_cube_count":13,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[579,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1176","image_path":"images/combination3d_1176.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1176_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1176_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1176_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_1176_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1176_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1176,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12}],"canvas_size":[600,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1177","image_path":"images/combination3d_1177.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1177_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1177_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1177_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1177_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1177_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1177,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,2],[1,0,3],[2,0,2],[3,0,2]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,0],[0,3,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,3],[0,2,3],[1,0,3],[1,1,2],[1,1,3],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[1,3,2],[2,0,3],[2,1,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":15}],"canvas_size":[613,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1178","image_path":"images/combination3d_1178.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1178_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1178_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1178_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1178_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1178_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1178,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,2,0],[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,1],[3,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,2,0],[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[555,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1179","image_path":"images/combination3d_1179.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1179_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1179_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1179_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1179_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1179_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1179,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[599,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1180","image_path":"images/combination3d_1180.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1180_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1180_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1180_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1180_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1180_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1180,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[596,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1181","image_path":"images/combination3d_1181.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1181_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1181_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1181_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1181_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1181_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1181,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[580,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1182","image_path":"images/combination3d_1182.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1182_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1182_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1182_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1182_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,5","question_id":"combination3d_1182_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1182,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[597,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1183","image_path":"images/combination3d_1183.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1183_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1183_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1183_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1183_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1183_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1183,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[615,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1184","image_path":"images/combination3d_1184.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1184_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1184_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1184_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1184_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_1184_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1184,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[582,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1185","image_path":"images/combination3d_1185.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1185_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1185_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1185_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1185_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1185_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1185,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],[[0,0,1],[0,1,1],[1,1,1],[1,2,1],[2,1,0],[2,1,1]]],"total_cube_count":13}],"canvas_size":[583,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1186","image_path":"images/combination3d_1186.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1186_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1186_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1186_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_1186_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1186_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1186,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[3,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,2],[0,2,3]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9}],"canvas_size":[591,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1187","image_path":"images/combination3d_1187.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1187_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1187_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1187_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1187_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1187_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1187,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[615,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1188","image_path":"images/combination3d_1188.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1188_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1188_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1188_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1188_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1188_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1188,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2]]],"total_cube_count":11}],"canvas_size":[617,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1189","image_path":"images/combination3d_1189.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1189_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1189_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1189_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1189_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1189_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1189,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,1],[1,2,1],[1,3,0],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,2],[2,2,2],[2,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[607,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1190","image_path":"images/combination3d_1190.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1190_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1190_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1190_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1190_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1190_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1190,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[602,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1191","image_path":"images/combination3d_1191.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1191_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1191_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1191_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1191_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1191_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1191,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,1],[0,2,2],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[586,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1192","image_path":"images/combination3d_1192.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1192_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1192_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1192_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1192_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1192_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1192,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2],[1,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,2,1],[0,3,1],[1,0,1],[1,0,2],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[589,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1193","image_path":"images/combination3d_1193.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1193_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1193_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1193_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1193_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1193_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1193,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9}],"canvas_size":[590,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1194","image_path":"images/combination3d_1194.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1194_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1194_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1194_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1194_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,6","question_id":"combination3d_1194_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1194,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,2,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[589,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1195","image_path":"images/combination3d_1195.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1195_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1195_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1195_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1195_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1195_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1195,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[571,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1196","image_path":"images/combination3d_1196.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1196_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1196_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1196_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1196_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1196_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1196,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,2]]],"total_cube_count":12}],"canvas_size":[581,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1197","image_path":"images/combination3d_1197.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1197_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1197_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1197_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1197_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1197_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1197,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[590,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1198","image_path":"images/combination3d_1198.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1198_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1198_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1198_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1198_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1198_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1198,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[561,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1199","image_path":"images/combination3d_1199.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1199_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1199_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1199_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1199_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1199_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1199,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[589,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1200","image_path":"images/combination3d_1200.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1200_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1200_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1200_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_1200_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1200_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1200,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,1,1],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[574,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1201","image_path":"images/combination3d_1201.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1201_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1201_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1201_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1201_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1201_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1201,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[1,0,2],[2,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,2],[1,0,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11}],"canvas_size":[589,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1202","image_path":"images/combination3d_1202.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1202_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1202_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1202_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1202_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1202_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1202,"target_cube_count":11,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,4,0],[2,0,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":10}],"canvas_size":[576,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1203","image_path":"images/combination3d_1203.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1203_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1203_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1203_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_1203_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1203_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1203,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,1],[1,0,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11}],"canvas_size":[598,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1204","image_path":"images/combination3d_1204.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1204_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1204_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1204_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1204_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1204_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1204,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,0,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,2,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,2,0],[0,2,1],[1,2,1],[1,3,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1],[2,3,2]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,3,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,4,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,1,2],[3,1,2]]],"total_cube_count":14}],"canvas_size":[602,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1205","image_path":"images/combination3d_1205.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1205_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1205_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1205_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1205_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1205_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1205,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[592,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1206","image_path":"images/combination3d_1206.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1206_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1206_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1206_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1206_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1206_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1206,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":14}],"canvas_size":[553,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1207","image_path":"images/combination3d_1207.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1207_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1207_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1207_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1207_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1207_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1207,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,1],[3,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[553,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1208","image_path":"images/combination3d_1208.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1208_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1208_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1208_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1208_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1208_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1208,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[619,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1209","image_path":"images/combination3d_1209.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1209_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1209_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1209_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1209_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1209_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1209,"target_cube_count":10,"target_cubes":[[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,2,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[559,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1210","image_path":"images/combination3d_1210.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1210_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1210_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1210_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1210_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1210_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1210,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]],[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":13}],"canvas_size":[587,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1211","image_path":"images/combination3d_1211.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1211_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1211_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1211_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1211_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1211_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1211,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,2,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[588,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1212","image_path":"images/combination3d_1212.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1212_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1212_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1212_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1212_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1212_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1212,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,3,0],[1,4,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,3],[0,1,4],[1,0,3]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[0,3,2],[1,3,0],[1,3,1],[1,4,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[1,3,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11}],"canvas_size":[615,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1213","image_path":"images/combination3d_1213.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1213_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1213_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1213_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1213_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1213_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1213,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[585,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1214","image_path":"images/combination3d_1214.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1214_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1214_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1214_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1214_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,5","question_id":"combination3d_1214_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1214,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[1,3,0],[1,3,1],[1,4,1],[2,1,1],[2,1,2],[2,2,1],[2,2,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,1],[2,0,2],[2,1,1],[2,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,1,1],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,1,1],[2,2,0],[2,2,1],[2,3,1]]],"total_cube_count":14}],"canvas_size":[606,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1215","image_path":"images/combination3d_1215.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1215_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1215_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1215_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1215_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1215_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1215,"target_cube_count":14,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[618,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1216","image_path":"images/combination3d_1216.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1216_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1216_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1216_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1216_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1216_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1216,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1],[3,1,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[556,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1217","image_path":"images/combination3d_1217.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1217_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1217_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1217_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1217_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1217_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1217,"target_cube_count":12,"target_cubes":[[0,3,0],[1,3,0],[1,4,0],[2,2,0],[2,2,1],[2,3,0],[2,4,0],[2,4,1],[3,0,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9}],"canvas_size":[619,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1218","image_path":"images/combination3d_1218.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1218_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1218_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1218_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_1218_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1218_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1218,"target_cube_count":8,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11}],"canvas_size":[617,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1219","image_path":"images/combination3d_1219.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1219_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1219_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1219_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1219_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1219_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1219,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[584,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1220","image_path":"images/combination3d_1220.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1220_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1220_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1220_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_1220_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1220_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1220,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[0,2,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,1],[0,3,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[557,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1221","image_path":"images/combination3d_1221.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1221_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1221_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1221_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1221_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1221_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1221,"target_cube_count":14,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,4,0],[1,4,1],[1,4,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,1]]],"total_cube_count":13}],"canvas_size":[612,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1222","image_path":"images/combination3d_1222.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1222_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1222_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1222_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1222_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1222_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1222,"target_cube_count":13,"target_cubes":[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[3,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[606,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1223","image_path":"images/combination3d_1223.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1223_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1223_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1223_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1223_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1223_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1223,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,0,2],[0,1,1],[1,1,0],[1,1,1],[1,2,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[563,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1224","image_path":"images/combination3d_1224.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1224_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1224_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1224_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1224_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1224_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1224,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,2],[0,3,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,2,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[598,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1225","image_path":"images/combination3d_1225.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1225_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1225_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1225_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1225_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1225_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1225,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[2,0,2],[2,0,3],[3,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[3,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1]]],"total_cube_count":9}],"canvas_size":[608,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1226","image_path":"images/combination3d_1226.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1226_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1226_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1226_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1226_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1226_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1226,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1],[2,2,2],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[2,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,1],[2,2,1],[2,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[553,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1227","image_path":"images/combination3d_1227.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1227_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1227_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1227_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1227_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1227_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1227,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[0,3,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":9}],"canvas_size":[565,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1228","image_path":"images/combination3d_1228.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1228_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1228_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1228_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1228_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1228_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1228,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,1],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[566,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1229","image_path":"images/combination3d_1229.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1229_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1229_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1229_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1229_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1229_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1229,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,2,1],[2,1,1],[2,2,1],[3,0,1],[3,1,1],[3,2,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[620,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1230","image_path":"images/combination3d_1230.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1230_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1230_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1230_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1230_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1230_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1230,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[598,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1231","image_path":"images/combination3d_1231.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1231_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1231_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1231_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1231_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_1231_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1231,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[566,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1232","image_path":"images/combination3d_1232.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1232_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1232_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1232_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1232_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1232_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1232,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,2],[0,3,0],[0,3,1],[0,3,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,0,2],[2,1,2]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0],[3,1,0],[3,2,0]]],"total_cube_count":12}],"canvas_size":[590,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1233","image_path":"images/combination3d_1233.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1233_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1233_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1233_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1233_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1233_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1233,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[0,4,2],[1,0,0],[1,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,1,0]]],"total_cube_count":8}],"canvas_size":[606,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1234","image_path":"images/combination3d_1234.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1234_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1234_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1234_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1234_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1234_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1234,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1]],[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":14}],"canvas_size":[604,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1235","image_path":"images/combination3d_1235.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1235_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1235_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1235_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1235_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1235_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1235,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[618,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1236","image_path":"images/combination3d_1236.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1236_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1236_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1236_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1236_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1236_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1236,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[1,4,1],[1,4,2],[1,5,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11}],"canvas_size":[569,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1237","image_path":"images/combination3d_1237.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1237_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1237_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1237_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1237_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1237_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1237,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[553,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1238","image_path":"images/combination3d_1238.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1238_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1238_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1238_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1238_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1238_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1238,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,4,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[2,3,1],[2,4,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,2]]],"total_cube_count":11}],"canvas_size":[559,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1239","image_path":"images/combination3d_1239.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1239_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1239_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1239_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1239_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_1239_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1239,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,2,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[609,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1240","image_path":"images/combination3d_1240.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1240_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1240_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1240_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1240_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1240_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1240,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[613,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1241","image_path":"images/combination3d_1241.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1241_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1241_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1241_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_1241_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1241_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1241,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":10}],"canvas_size":[560,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1242","image_path":"images/combination3d_1242.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1242_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1242_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1242_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1242_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1242_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1242,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[3,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[1,2,0],[1,2,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,1,0],[1,1,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[616,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1243","image_path":"images/combination3d_1243.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1243_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1243_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1243_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_1243_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1243_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1243,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[585,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1244","image_path":"images/combination3d_1244.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1244_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1244_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1244_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1244_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1244_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1244,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1]]],"total_cube_count":9}],"canvas_size":[618,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1245","image_path":"images/combination3d_1245.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1245_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1245_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1245_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1245_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_1245_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1245,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[0,1,2],[1,0,2],[1,1,1],[1,1,2],[1,2,2],[1,3,2],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[571,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1246","image_path":"images/combination3d_1246.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1246_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1246_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1246_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1246_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1246_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1246,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15}],"canvas_size":[562,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1247","image_path":"images/combination3d_1247.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1247_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1247_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1247_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_1247_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1247_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1247,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[614,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1248","image_path":"images/combination3d_1248.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1248_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1248_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1248_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1248_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1248_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1248,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1]],[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1]],[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,3,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,0,0],[3,0,0]]],"total_cube_count":13}],"canvas_size":[614,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1249","image_path":"images/combination3d_1249.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1249_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1249_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1249_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_1249_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1249_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1249,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,0,2],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":13}],"canvas_size":[568,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1250","image_path":"images/combination3d_1250.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1250_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1250_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1250_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_1250_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1250_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1250,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":10}],"canvas_size":[551,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1251","image_path":"images/combination3d_1251.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1251_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1251_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1251_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_1251_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1251_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1251,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,1],[1,1,3]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[588,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1252","image_path":"images/combination3d_1252.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1252_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1252_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1252_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1252_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1252_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1252,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[576,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1253","image_path":"images/combination3d_1253.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1253_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1253_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1253_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1253_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1253_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1253,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,2,1],[3,1,0]]],"total_cube_count":10}],"canvas_size":[605,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1254","image_path":"images/combination3d_1254.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1254_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1254_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1254_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1254_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1254_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1254,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[2,1,0],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[599,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1255","image_path":"images/combination3d_1255.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1255_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1255_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1255_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1255_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1255_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1255,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1],[2,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[620,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1256","image_path":"images/combination3d_1256.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1256_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1256_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1256_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1256_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1256_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1256,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,2,0],[0,2,1],[1,2,1],[2,0,1],[2,1,1],[2,2,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":9}],"canvas_size":[615,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1257","image_path":"images/combination3d_1257.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1257_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1257_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1257_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1257_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1257_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1257,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[567,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1258","image_path":"images/combination3d_1258.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1258_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1258_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1258_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1258_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1258_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1258,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":14}],"canvas_size":[599,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1259","image_path":"images/combination3d_1259.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1259_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1259_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1259_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_1259_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1259_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1259,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[561,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1260","image_path":"images/combination3d_1260.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1260_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1260_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1260_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1260_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1260_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1260,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,1,1],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[559,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1261","image_path":"images/combination3d_1261.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1261_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1261_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1261_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1261_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,5","question_id":"combination3d_1261_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1261,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[1,0,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[574,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1262","image_path":"images/combination3d_1262.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1262_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1262_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1262_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1262_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1262_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1262,"target_cube_count":9,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[1,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10}],"canvas_size":[571,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1263","image_path":"images/combination3d_1263.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1263_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1263_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1263_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_1263_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1263_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1263,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[565,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1264","image_path":"images/combination3d_1264.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1264_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1264_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1264_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1264_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1264_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1264,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[1,2,2]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":12}],"canvas_size":[550,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1265","image_path":"images/combination3d_1265.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1265_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1265_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1265_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1265_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1265_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1265,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,1],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[576,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1266","image_path":"images/combination3d_1266.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1266_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1266_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1266_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1266_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1266_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1266,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,2],[1,0,2],[1,1,2],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":11}],"canvas_size":[558,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1267","image_path":"images/combination3d_1267.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1267_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1267_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1267_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1267_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1267_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1267,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[2,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[560,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1268","image_path":"images/combination3d_1268.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1268_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1268_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1268_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1268_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1268_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1268,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,4,0],[1,4,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,3],[1,1,2],[1,1,3],[2,0,3],[2,1,2],[2,1,3],[2,2,0],[2,2,1],[2,2,2],[3,0,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13}],"canvas_size":[597,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1269","image_path":"images/combination3d_1269.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1269_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1269_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1269_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1269_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_1269_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1269,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[0,3,4],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[579,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1270","image_path":"images/combination3d_1270.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1270_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1270_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1270_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1270_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1270_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1270,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[2,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,2]]],"total_cube_count":13}],"canvas_size":[594,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1271","image_path":"images/combination3d_1271.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1271_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1271_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1271_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1271_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_1271_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1271,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[578,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1272","image_path":"images/combination3d_1272.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1272_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1272_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1272_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1272_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1272_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1272,"target_cube_count":8,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[4,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[618,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1273","image_path":"images/combination3d_1273.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1273_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1273_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1273_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,5","question_id":"combination3d_1273_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1273_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1273,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,2,1],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10}],"canvas_size":[565,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1274","image_path":"images/combination3d_1274.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1274_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1274_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1274_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1274_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1274_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1274,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[1,0,0],[1,1,2],[1,1,3],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,0,1],[3,0,2],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":15}],"canvas_size":[582,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1275","image_path":"images/combination3d_1275.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1275_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1275_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1275_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1275_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1275_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1275,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9}],"canvas_size":[581,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1276","image_path":"images/combination3d_1276.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1276_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1276_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1276_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1276_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1276_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1276,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,2],[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,0,2],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,2,2],[1,0,1]]],"total_cube_count":14}],"canvas_size":[578,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1277","image_path":"images/combination3d_1277.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1277_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1277_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1277_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1277_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1277_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1277,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8}],"canvas_size":[557,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1278","image_path":"images/combination3d_1278.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1278_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1278_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1278_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1278_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1278_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1278,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,1],[1,2,0],[1,2,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11}],"canvas_size":[612,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1279","image_path":"images/combination3d_1279.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1279_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1279_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1279_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1279_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1279_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1279,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[596,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1280","image_path":"images/combination3d_1280.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1280_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1280_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1280_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1280_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1280_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1280,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":13}],"canvas_size":[578,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1281","image_path":"images/combination3d_1281.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1281_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1281_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1281_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1281_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1281_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1281,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[556,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1282","image_path":"images/combination3d_1282.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1282_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1282_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1282_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1282_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1282_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1282,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[591,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1283","image_path":"images/combination3d_1283.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1283_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1283_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1283_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1283_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1283_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1283,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":11}],"canvas_size":[613,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1284","image_path":"images/combination3d_1284.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1284_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1284_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1284_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1284_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1284_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1284,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[582,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1285","image_path":"images/combination3d_1285.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1285_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1285_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1285_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1285_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1285_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1285,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[592,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1286","image_path":"images/combination3d_1286.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1286_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1286_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1286_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1286_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1286_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1286,"target_cube_count":8,"target_cubes":[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8}],"canvas_size":[607,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1287","image_path":"images/combination3d_1287.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1287_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1287_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1287_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1287_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1287_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1287,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1],[2,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[555,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1288","image_path":"images/combination3d_1288.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1288_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1288_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1288_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1288_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1288_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1288,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,0,2],[2,1,1],[2,1,2],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[610,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1289","image_path":"images/combination3d_1289.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1289_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1289_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1289_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1289_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1289_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1289,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10}],"canvas_size":[595,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1290","image_path":"images/combination3d_1290.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1290_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1290_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1290_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1290_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1290_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1290,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,0,2],[3,0,3],[3,1,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,2],[2,0,0],[2,1,0],[2,2,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,0,3],[2,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,2,1],[0,3,1],[1,1,1],[1,2,1],[1,3,1],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":14}],"canvas_size":[599,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1291","image_path":"images/combination3d_1291.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1291_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1291_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1291_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1291_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1291_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1291,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,3,0],[1,4,0],[1,4,1]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,1,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[602,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1292","image_path":"images/combination3d_1292.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1292_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1292_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1292_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,5","question_id":"combination3d_1292_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1292_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1292,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[588,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1293","image_path":"images/combination3d_1293.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1293_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1293_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1293_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1293_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1293_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1293,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[596,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1294","image_path":"images/combination3d_1294.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1294_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1294_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1294_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1294_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_1294_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1294,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[2,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,1,0],[1,3,0],[1,4,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[0,4,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,4,1]]],"total_cube_count":15}],"canvas_size":[562,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1295","image_path":"images/combination3d_1295.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1295_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1295_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1295_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1295_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1295_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1295,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,5,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10}],"canvas_size":[610,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1296","image_path":"images/combination3d_1296.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1296_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1296_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1296_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1296_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1296_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1296,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,2],[1,1,0],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,2,1],[2,2,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0],[2,0,1],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[606,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1297","image_path":"images/combination3d_1297.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1297_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1297_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1297_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1297_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1297_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1297,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[2,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[2,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[574,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1298","image_path":"images/combination3d_1298.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1298_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1298_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1298_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1298_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1298_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1298,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[2,3,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,0,2],[2,1,1]]],"total_cube_count":13}],"canvas_size":[591,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1299","image_path":"images/combination3d_1299.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1299_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1299_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1299_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1299_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1299_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1299,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[596,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1300","image_path":"images/combination3d_1300.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1300_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1300_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1300_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,5","question_id":"combination3d_1300_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1300_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1300,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0],[1,3,1],[1,4,0],[1,4,1]]],"total_cube_count":14}],"canvas_size":[604,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1301","image_path":"images/combination3d_1301.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1301_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1301_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1301_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1301_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1301_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1301,"target_cube_count":14,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,2,2],[2,0,1]]],"total_cube_count":12}],"canvas_size":[611,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1302","image_path":"images/combination3d_1302.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1302_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1302_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1302_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1302_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1302_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1302,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,1,2],[4,1,0],[4,1,1],[4,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,2],[1,2,2]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":14}],"canvas_size":[596,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1303","image_path":"images/combination3d_1303.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1303_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1303_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1303_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1303_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1303_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1303,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,4,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,2],[1,4,0],[1,4,1],[1,4,2]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,2,0],[0,2,1],[0,2,3],[1,0,4],[1,1,4],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[1,4,2]]],"total_cube_count":14}],"canvas_size":[600,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1304","image_path":"images/combination3d_1304.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1304_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1304_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1304_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1304_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1304_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1304,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[1,4,1],[1,4,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,0,2],[2,1,1],[2,1,2],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,1],[2,2,1],[3,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[3,2,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11}],"canvas_size":[571,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1305","image_path":"images/combination3d_1305.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1305_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1305_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1305_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_1305_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1305_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1305,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[3,2,0],[3,2,1],[3,2,2],[3,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":8}],"canvas_size":[611,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1306","image_path":"images/combination3d_1306.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1306_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1306_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1306_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1306_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1306_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1306,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,1]],[[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,3,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]]],"total_cube_count":12}],"canvas_size":[566,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1307","image_path":"images/combination3d_1307.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1307_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1307_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1307_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1307_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1307_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1307,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,5,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[3,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9}],"canvas_size":[613,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1308","image_path":"images/combination3d_1308.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1308_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1308_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1308_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1308_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1308_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1308,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,1,1]],[[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,2,1],[1,2,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[613,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1309","image_path":"images/combination3d_1309.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1309_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1309_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1309_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1309_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1309_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1309,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,2,1],[2,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[580,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1310","image_path":"images/combination3d_1310.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1310_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1310_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1310_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1310_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1310_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1310,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[2,1,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[568,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1311","image_path":"images/combination3d_1311.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1311_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1311_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1311_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,5","question_id":"combination3d_1311_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1311_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1311,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,1,0],[4,0,0],[4,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[614,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1312","image_path":"images/combination3d_1312.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1312_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1312_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1312_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1312_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1312_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1312,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,1,1]]],"total_cube_count":13}],"canvas_size":[604,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1313","image_path":"images/combination3d_1313.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1313_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1313_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1313_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_1313_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1313_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1313,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,1,1],[2,0,0],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[4,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,1],[2,0,2],[2,1,1],[3,1,1],[4,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,1],[4,1,1]]],"total_cube_count":11}],"canvas_size":[600,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1314","image_path":"images/combination3d_1314.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1314_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1314_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1314_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1314_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1314_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1314,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[599,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1315","image_path":"images/combination3d_1315.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1315_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1315_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1315_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1315_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1315_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1315,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[576,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1316","image_path":"images/combination3d_1316.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1316_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1316_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1316_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1316_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1316_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1316,"target_cube_count":9,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0],[2,4,0],[2,5,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":9}],"canvas_size":[590,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1317","image_path":"images/combination3d_1317.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1317_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1317_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1317_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1317_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1317_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1317,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,0,2],[3,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[585,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1318","image_path":"images/combination3d_1318.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1318_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1318_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1318_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1318_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1318_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1318,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,2],[0,2,0],[0,2,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[601,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1319","image_path":"images/combination3d_1319.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1319_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1319_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1319_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1319_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1319_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1319,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[568,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1320","image_path":"images/combination3d_1320.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1320_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1320_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1320_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1320_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1320_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1320,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[618,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1321","image_path":"images/combination3d_1321.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1321_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1321_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1321_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1321_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1321_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1321,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[1,2,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10}],"canvas_size":[602,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1322","image_path":"images/combination3d_1322.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1322_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1322_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1322_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_1322_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1322_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1322,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,1,1],[3,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,3]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[611,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1323","image_path":"images/combination3d_1323.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1323_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1323_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1323_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1323_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_1323_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1323,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[610,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1324","image_path":"images/combination3d_1324.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1324_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1324_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1324_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1324_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1324_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1324,"target_cube_count":11,"target_cubes":[[0,3,0],[0,4,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[574,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1325","image_path":"images/combination3d_1325.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1325_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1325_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1325_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1325_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1325_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1325,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":8}],"canvas_size":[612,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1326","image_path":"images/combination3d_1326.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1326_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1326_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1326_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1326_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1326_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1326,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,3,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[579,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1327","image_path":"images/combination3d_1327.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1327_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1327_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1327_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1327_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1327_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1327,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[2,3,2],[2,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[1,1,2],[1,1,3]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":12}],"canvas_size":[568,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1328","image_path":"images/combination3d_1328.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1328_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1328_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1328_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1328_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1328_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1328,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,2,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":9}],"canvas_size":[601,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1329","image_path":"images/combination3d_1329.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1329_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1329_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1329_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1329_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1329_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1329,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[594,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1330","image_path":"images/combination3d_1330.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1330_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1330_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1330_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1330_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1330_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1330,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,1,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[3,2,1],[3,2,2]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[3,0,2],[3,1,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[617,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1331","image_path":"images/combination3d_1331.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1331_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1331_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1331_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1331_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1331_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1331,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[3,2,0],[3,2,1],[3,2,2],[3,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0],[4,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[2,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[556,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1332","image_path":"images/combination3d_1332.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1332_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1332_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1332_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1332_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1332_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1332,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":14}],"canvas_size":[612,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1333","image_path":"images/combination3d_1333.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1333_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1333_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1333_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1333_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_1333_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1333,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[2,0,1]]],"total_cube_count":8}],"canvas_size":[608,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1334","image_path":"images/combination3d_1334.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1334_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1334_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1334_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1334_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1334_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1334,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[617,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1335","image_path":"images/combination3d_1335.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1335_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1335_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1335_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1335_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1335_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1335,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8}],"canvas_size":[615,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1336","image_path":"images/combination3d_1336.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1336_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1336_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1336_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1336_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1336_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1336,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,1,0],[3,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[618,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1337","image_path":"images/combination3d_1337.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1337_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1337_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1337_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1337_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1337_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1337,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1],[4,1,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":14}],"canvas_size":[594,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1338","image_path":"images/combination3d_1338.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1338_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1338_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1338_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1338_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1338_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1338,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1]]],"total_cube_count":8}],"canvas_size":[576,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1339","image_path":"images/combination3d_1339.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1339_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1339_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1339_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1339_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1339_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1339,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,0],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[595,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1340","image_path":"images/combination3d_1340.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1340_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1340_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1340_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1340_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1340_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1340,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0],[2,3,1],[2,3,2],[2,3,3],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[607,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1341","image_path":"images/combination3d_1341.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1341_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1341_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1341_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1341_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1341_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1341,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":10}],"canvas_size":[558,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1342","image_path":"images/combination3d_1342.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1342_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1342_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1342_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1342_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1342_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1342,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[4,0,0],[4,0,1],[4,1,0],[4,1,1],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[1,1,1],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[592,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1343","image_path":"images/combination3d_1343.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1343_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1343_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1343_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1343_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1343_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1343,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[3,0,1],[3,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[2,1,1],[3,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0]]],"total_cube_count":11}],"canvas_size":[603,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1344","image_path":"images/combination3d_1344.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1344_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1344_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1344_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_1344_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1344_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1344,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[2,0,2]]],"total_cube_count":12}],"canvas_size":[562,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1345","image_path":"images/combination3d_1345.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1345_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1345_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1345_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1345_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1345_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1345,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,2]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[588,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1346","image_path":"images/combination3d_1346.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1346_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1346_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1346_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1346_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1346_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1346,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0]],[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":12}],"canvas_size":[612,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1347","image_path":"images/combination3d_1347.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1347_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1347_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1347_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,5","question_id":"combination3d_1347_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1347_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1347,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,2,0],[1,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[599,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1348","image_path":"images/combination3d_1348.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1348_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1348_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1348_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1348_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1348_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1348,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[550,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1349","image_path":"images/combination3d_1349.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1349_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1349_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1349_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1349_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1349_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1349,"target_cube_count":12,"target_cubes":[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[612,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1350","image_path":"images/combination3d_1350.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1350_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1350_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1350_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1350_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1350_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1350,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":8}],"canvas_size":[570,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1351","image_path":"images/combination3d_1351.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1351_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1351_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1351_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1351_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1351_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1351,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,3,0],[0,3,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[588,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1352","image_path":"images/combination3d_1352.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1352_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1352_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1352_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_1352_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1352_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1352,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[576,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1353","image_path":"images/combination3d_1353.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1353_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1353_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1353_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1353_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1353_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1353,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1]]],"total_cube_count":8}],"canvas_size":[618,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1354","image_path":"images/combination3d_1354.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1354_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1354_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1354_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1354_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1354_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1354,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]]],"total_cube_count":9}],"canvas_size":[597,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1355","image_path":"images/combination3d_1355.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1355_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1355_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1355_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1355_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1355_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1355,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13}],"canvas_size":[581,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1356","image_path":"images/combination3d_1356.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1356_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1356_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1356_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1356_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_1356_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1356,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":9}],"canvas_size":[604,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1357","image_path":"images/combination3d_1357.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1357_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1357_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1357_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1357_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1357_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1357,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[551,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1358","image_path":"images/combination3d_1358.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1358_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1358_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1358_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1358_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1358_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1358,"target_cube_count":8,"target_cubes":[[0,2,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[610,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1359","image_path":"images/combination3d_1359.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1359_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1359_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1359_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1359_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1359_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1359,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,2],[1,1,2],[1,2,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[577,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1360","image_path":"images/combination3d_1360.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1360_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1360_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1360_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_1360_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1360_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1360,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[3,1,1],[4,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":10}],"canvas_size":[564,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1361","image_path":"images/combination3d_1361.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1361_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1361_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1361_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1361_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1361_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1361,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,0,1],[2,1,1],[2,1,2],[2,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0],[3,1,0],[4,0,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[556,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1362","image_path":"images/combination3d_1362.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1362_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1362_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1362_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1362_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1362_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1362,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[3,2,1],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[575,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1363","image_path":"images/combination3d_1363.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1363_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1363_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1363_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1363_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1363_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1363,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,2,0],[1,3,0],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2],[1,3,3]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[573,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1364","image_path":"images/combination3d_1364.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1364_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1364_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1364_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1364_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1364_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1364,"target_cube_count":11,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":11}],"canvas_size":[613,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1365","image_path":"images/combination3d_1365.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1365_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1365_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1365_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1365_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1365_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1365,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,2],[1,2,2]],[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[616,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1366","image_path":"images/combination3d_1366.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1366_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1366_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1366_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1366_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1366_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1366,"target_cube_count":12,"target_cubes":[[0,2,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[602,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1367","image_path":"images/combination3d_1367.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1367_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1367_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1367_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1367_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,5","question_id":"combination3d_1367_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1367,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[0,4,0],[0,4,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[577,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1368","image_path":"images/combination3d_1368.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1368_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1368_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1368_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1368_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1368_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1368,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[587,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1369","image_path":"images/combination3d_1369.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1369_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1369_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1369_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_1369_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1369_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1369,"target_cube_count":10,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[583,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1370","image_path":"images/combination3d_1370.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1370_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1370_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1370_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1370_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1370_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1370,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,3,0],[2,4,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[2,3,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[602,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1371","image_path":"images/combination3d_1371.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1371_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1371_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1371_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1371_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1371_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1371,"target_cube_count":12,"target_cubes":[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[563,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1372","image_path":"images/combination3d_1372.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1372_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1372_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1372_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1372_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1372_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1372,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[555,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1373","image_path":"images/combination3d_1373.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1373_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1373_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1373_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1373_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1373_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1373,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,3,0],[0,3,1],[0,3,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,3,0],[0,3,1],[1,1,1],[1,2,1],[1,3,1],[2,3,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[551,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1374","image_path":"images/combination3d_1374.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1374_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1374_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1374_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1374_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1374_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1374,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":8}],"canvas_size":[557,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1375","image_path":"images/combination3d_1375.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1375_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1375_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1375_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1375_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1375_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1375,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1],[3,0,2],[4,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[609,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1376","image_path":"images/combination3d_1376.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1376_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1376_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1376_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1376_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1376_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1376,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[568,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1377","image_path":"images/combination3d_1377.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1377_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1377_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1377_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1377_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1377_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1377,"target_cube_count":8,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,1,2],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,2,1],[2,2,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[3,1,0]]],"total_cube_count":9}],"canvas_size":[551,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1378","image_path":"images/combination3d_1378.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1378_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1378_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1378_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1378_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1378_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1378,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,1,0],[2,1,1]]],"total_cube_count":13}],"canvas_size":[582,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1379","image_path":"images/combination3d_1379.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1379_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1379_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1379_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1379_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1379_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1379,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,2,0],[3,2,1],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[610,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1380","image_path":"images/combination3d_1380.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1380_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1380_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1380_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1380_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1380_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1380,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":11}],"canvas_size":[561,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1381","image_path":"images/combination3d_1381.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1381_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1381_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1381_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1381_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1381_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1381,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,2,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,2],[1,2,3],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[603,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1382","image_path":"images/combination3d_1382.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1382_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1382_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1382_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_1382_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1382_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1382,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,1,2],[3,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[3,2,0],[4,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[565,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1383","image_path":"images/combination3d_1383.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1383_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1383_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1383_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1383_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1383_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1383,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,3,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,2,0]]],"total_cube_count":13}],"canvas_size":[589,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1384","image_path":"images/combination3d_1384.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1384_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1384_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1384_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1384_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1384_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1384,"target_cube_count":13,"target_cubes":[[0,2,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[569,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1385","image_path":"images/combination3d_1385.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1385_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1385_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1385_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_1385_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1385_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1385,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[1,1,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1],[4,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1]]],"total_cube_count":12}],"canvas_size":[573,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1386","image_path":"images/combination3d_1386.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1386_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1386_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1386_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,5","question_id":"combination3d_1386_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1386_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1386,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,0],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,1,1],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13}],"canvas_size":[559,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1387","image_path":"images/combination3d_1387.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1387_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1387_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1387_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1387_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1387_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1387,"target_cube_count":12,"target_cubes":[[0,3,0],[0,4,0],[0,4,1],[0,5,0],[1,4,0],[1,5,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[574,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1388","image_path":"images/combination3d_1388.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1388_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1388_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1388_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1388_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1388_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1388,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,0,1],[0,1,1],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[556,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1389","image_path":"images/combination3d_1389.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1389_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1389_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1389_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1389_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1389_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1389,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":8}],"canvas_size":[561,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1390","image_path":"images/combination3d_1390.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1390_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1390_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1390_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_1390_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1390_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1390,"target_cube_count":8,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,1],[1,3,2],[2,0,1],[2,3,1],[2,3,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,2]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":15}],"canvas_size":[567,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1391","image_path":"images/combination3d_1391.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1391_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1391_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1391_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1391_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1391_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1391,"target_cube_count":14,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,2,0],[2,3,0],[2,3,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":14}],"canvas_size":[583,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1392","image_path":"images/combination3d_1392.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1392_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1392_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1392_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1392_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1392_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1392,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[598,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1393","image_path":"images/combination3d_1393.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1393_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1393_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1393_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1393_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1393_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1393,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[600,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1394","image_path":"images/combination3d_1394.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1394_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1394_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1394_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1394_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1394_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1394,"target_cube_count":11,"target_cubes":[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,1,1],[1,1,2],[1,2,2],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1]]],"total_cube_count":14}],"canvas_size":[563,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1395","image_path":"images/combination3d_1395.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1395_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1395_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1395_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1395_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1395_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1395,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[2,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,1],[1,3,2],[1,3,3],[1,4,2],[1,5,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[559,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1396","image_path":"images/combination3d_1396.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1396_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1396_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1396_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_1396_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1396_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1396,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":10}],"canvas_size":[559,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1397","image_path":"images/combination3d_1397.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1397_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1397_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1397_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1397_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1397_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1397,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[4,0,0],[4,1,0],[5,1,0],[5,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,1,2]]],"total_cube_count":14}],"canvas_size":[593,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1398","image_path":"images/combination3d_1398.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1398_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1398_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1398_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1398_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1398_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1398,"target_cube_count":14,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[616,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1399","image_path":"images/combination3d_1399.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1399_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1399_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1399_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1399_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1399_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1399,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,2],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2],[4,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0]]],"total_cube_count":12}],"canvas_size":[571,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1400","image_path":"images/combination3d_1400.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1400_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1400_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1400_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1400_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1400_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1400,"target_cube_count":12,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[606,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1401","image_path":"images/combination3d_1401.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1401_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1401_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1401_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1401_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1401_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1401,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":8}],"canvas_size":[552,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1402","image_path":"images/combination3d_1402.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1402_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1402_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1402_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_1402_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1402_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1402,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,2,1],[1,3,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[590,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1403","image_path":"images/combination3d_1403.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1403_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1403_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1403_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1403_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1403_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1403,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[565,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1404","image_path":"images/combination3d_1404.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1404_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1404_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1404_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1404_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1404_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1404,"target_cube_count":8,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,0,3],[1,1,2],[1,2,2]]],"total_cube_count":9}],"canvas_size":[604,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1405","image_path":"images/combination3d_1405.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1405_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1405_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1405_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1405_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1405_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1405,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1]],[[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,1],[4,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1]],[[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":14}],"canvas_size":[573,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1406","image_path":"images/combination3d_1406.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1406_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1406_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1406_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1406_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1406_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1406,"target_cube_count":13,"target_cubes":[[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[561,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1407","image_path":"images/combination3d_1407.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1407_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1407_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1407_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1407_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_1407_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1407,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[612,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1408","image_path":"images/combination3d_1408.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1408_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1408_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1408_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1408_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1408_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1408,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[554,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1409","image_path":"images/combination3d_1409.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1409_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1409_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1409_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1409_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_1409_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1409,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[0,3,0],[0,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":10}],"canvas_size":[587,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1410","image_path":"images/combination3d_1410.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1410_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1410_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1410_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1410_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1410_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1410,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,4]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[4,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,1],[3,0,1],[4,0,1]]],"total_cube_count":9}],"canvas_size":[563,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1411","image_path":"images/combination3d_1411.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1411_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1411_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1411_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1411_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1411_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1411,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,0,2],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,0,2],[1,1,1]]],"total_cube_count":13}],"canvas_size":[610,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1412","image_path":"images/combination3d_1412.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1412_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1412_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1412_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_1412_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1412_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1412,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[608,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1413","image_path":"images/combination3d_1413.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1413_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1413_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1413_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1413_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1413_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1413,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,1,1],[2,1,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":10}],"canvas_size":[567,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1414","image_path":"images/combination3d_1414.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1414_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1414_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1414_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1414_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_1414_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1414,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,1],[1,1,2],[2,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,2],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,2,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13}],"canvas_size":[619,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1415","image_path":"images/combination3d_1415.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1415_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1415_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1415_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1415_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1415_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1415,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,0,1],[3,1,1],[3,1,2],[4,1,1],[4,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[562,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1416","image_path":"images/combination3d_1416.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1416_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1416_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1416_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1416_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1416_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1416,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,3],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,2,0],[2,3,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14}],"canvas_size":[590,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1417","image_path":"images/combination3d_1417.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1417_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1417_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1417_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1417_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1417_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1417,"target_cube_count":13,"target_cubes":[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[2,3,0],[2,4,0],[2,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,1],[2,1,0],[2,1,1],[2,1,2],[2,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,3,1],[1,1,1],[1,2,0],[1,2,1],[1,3,1],[1,3,2],[2,0,1],[2,1,1],[2,3,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[552,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1418","image_path":"images/combination3d_1418.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1418_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1418_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1418_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_1418_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1418_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1418,"target_cube_count":13,"target_cubes":[[0,1,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,3,0],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,4,0],[2,4,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[615,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1419","image_path":"images/combination3d_1419.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1419_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1419_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1419_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1419_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_1419_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1419,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[2,0,2],[2,2,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,1],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,2,1],[1,3,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":14}],"canvas_size":[603,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1420","image_path":"images/combination3d_1420.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1420_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1420_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1420_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1420_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1420_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1420,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[557,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1421","image_path":"images/combination3d_1421.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1421_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1421_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1421_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1421_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1421_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1421,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,0,1]],[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[577,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1422","image_path":"images/combination3d_1422.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1422_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1422_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1422_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1422_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1422_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1422,"target_cube_count":11,"target_cubes":[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":9}],"canvas_size":[607,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1423","image_path":"images/combination3d_1423.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1423_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1423_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1423_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_1423_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1423_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1423,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":12}],"canvas_size":[556,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1424","image_path":"images/combination3d_1424.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1424_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1424_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1424_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1424_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1424_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1424,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,4,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,2],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,1],[2,1,0],[2,1,1],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":12}],"canvas_size":[591,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1425","image_path":"images/combination3d_1425.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1425_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1425_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1425_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1425_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1425_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1425,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,2],[1,1,1],[1,1,2]],[[0,1,1],[1,1,1],[2,0,0],[2,0,1],[2,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[0,0,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[2,1,2],[2,1,3],[2,1,4]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,2],[0,1,2],[0,2,2],[0,3,1],[0,3,2],[1,3,0],[1,3,1],[1,3,2]]],"total_cube_count":13}],"canvas_size":[560,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1426","image_path":"images/combination3d_1426.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1426_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1426_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1426_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1426_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1426_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1426,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1],[3,2,2],[3,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,2],[2,0,3],[3,0,2],[3,0,3]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,1],[2,2,1],[2,3,1],[3,2,1],[3,3,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[3,2,0],[3,3,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[550,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1427","image_path":"images/combination3d_1427.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1427_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1427_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1427_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1427_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1427_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1427,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[3,2,0],[3,2,1],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,3],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,2]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,0,2],[0,0,3],[1,0,1],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13}],"canvas_size":[616,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1428","image_path":"images/combination3d_1428.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1428_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1428_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1428_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1428_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1428_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1428,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[564,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1429","image_path":"images/combination3d_1429.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1429_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1429_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1429_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1429_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1429_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1429,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,2]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13}],"canvas_size":[586,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1430","image_path":"images/combination3d_1430.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1430_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1430_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1430_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1430_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1430_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1430,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,2],[2,0,2],[2,1,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[617,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1431","image_path":"images/combination3d_1431.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1431_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1431_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1431_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1431_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1431_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1431,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1],[3,2,2],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,2,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10}],"canvas_size":[611,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1432","image_path":"images/combination3d_1432.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1432_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1432_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1432_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1432_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,6","question_id":"combination3d_1432_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1432,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[563,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1433","image_path":"images/combination3d_1433.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1433_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1433_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1433_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1433_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1433_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1433,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[550,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1434","image_path":"images/combination3d_1434.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1434_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1434_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1434_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1434_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1434_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1434,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,3]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1]]],"total_cube_count":10}],"canvas_size":[587,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1435","image_path":"images/combination3d_1435.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1435_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1435_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1435_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1435_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_1435_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1435,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,1,0],[2,0,1],[2,1,0],[3,0,1],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,2],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,1],[2,1,2],[2,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,3],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[590,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1436","image_path":"images/combination3d_1436.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1436_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1436_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1436_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_1436_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1436_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1436,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2],[1,1,1],[1,2,2]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[1,3,1],[2,1,0],[2,1,1],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2]],[[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,1,0],[2,1,1]]],"total_cube_count":14}],"canvas_size":[577,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1437","image_path":"images/combination3d_1437.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1437_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1437_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1437_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1437_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1437_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1437,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0]]],"total_cube_count":11}],"canvas_size":[607,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1438","image_path":"images/combination3d_1438.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1438_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1438_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1438_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1438_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1438_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1438,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1]]],"total_cube_count":9}],"canvas_size":[614,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1439","image_path":"images/combination3d_1439.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1439_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1439_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1439_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1439_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1439_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1439,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,0,2]],[[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,3,1],[0,3,2],[1,0,1],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,1,0],[1,2,1],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[580,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1440","image_path":"images/combination3d_1440.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1440_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1440_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1440_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1440_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1440_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1440,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[585,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1441","image_path":"images/combination3d_1441.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1441_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1441_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1441_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1441_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1441_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1441,"target_cube_count":11,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[1,2,1],[1,3,1],[2,2,1],[3,1,1],[3,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[3,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":14}],"canvas_size":[552,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1442","image_path":"images/combination3d_1442.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1442_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1442_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1442_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1442_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1442_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1442,"target_cube_count":13,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,2,0],[3,3,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,2,0],[3,3,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[3,2,0],[3,2,2],[3,2,3]]],"total_cube_count":13}],"canvas_size":[581,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1443","image_path":"images/combination3d_1443.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1443_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1443_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1443_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1443_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1443_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1443,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,3,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,3],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,3,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[567,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1444","image_path":"images/combination3d_1444.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1444_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1444_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1444_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1444_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1444_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1444,"target_cube_count":11,"target_cubes":[[0,1,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10}],"canvas_size":[581,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1445","image_path":"images/combination3d_1445.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1445_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1445_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1445_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1445_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1445_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1445,"target_cube_count":9,"target_cubes":[[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[3,1,1],[3,2,0],[3,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[0,3,1],[0,3,2],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12}],"canvas_size":[593,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1446","image_path":"images/combination3d_1446.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1446_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1446_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1446_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1446_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1446_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1446,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,2,0],[0,2,1],[1,1,1],[1,2,1],[2,0,1],[2,0,2],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0],[2,4,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,2],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[561,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1447","image_path":"images/combination3d_1447.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1447_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1447_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1447_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1447_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1447_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1447,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9}],"canvas_size":[605,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1448","image_path":"images/combination3d_1448.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1448_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1448_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1448_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1448_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1448_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1448,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[1,0,2],[1,0,3]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3]]],"total_cube_count":15}],"canvas_size":[562,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1449","image_path":"images/combination3d_1449.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1449_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1449_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1449_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1449_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1449_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1449,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":9}],"canvas_size":[620,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1450","image_path":"images/combination3d_1450.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1450_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1450_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1450_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1450_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1450_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1450,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,3,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[595,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1451","image_path":"images/combination3d_1451.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1451_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1451_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1451_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1451_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1451_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1451,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,0,2],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,2],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,1,1],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[584,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1452","image_path":"images/combination3d_1452.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1452_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1452_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1452_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1452_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1452_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1452,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,2,0],[2,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,2,0],[2,2,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[1,3,0],[1,3,1],[1,3,2],[2,2,0],[2,2,2],[2,3,0],[2,3,2]]],"total_cube_count":14}],"canvas_size":[587,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1453","image_path":"images/combination3d_1453.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1453_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1453_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1453_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1453_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1453_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1453,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,2,2],[2,2,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":12}],"canvas_size":[588,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1454","image_path":"images/combination3d_1454.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1454_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1454_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1454_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1454_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1454_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1454,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1]]],"total_cube_count":8}],"canvas_size":[619,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1455","image_path":"images/combination3d_1455.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1455_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1455_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1455_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1455_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1455_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1455,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,2],[0,3,0],[0,3,1],[0,3,2]],[[0,1,0],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,1,1],[3,0,1],[3,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3]],[[0,0,1],[0,0,2],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3]],[[0,0,1],[0,0,2],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":13}],"canvas_size":[609,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1456","image_path":"images/combination3d_1456.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1456_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1456_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1456_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1456_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1456_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1456,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,2],[1,2,2],[1,2,3],[1,3,2],[2,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[593,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1457","image_path":"images/combination3d_1457.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1457_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1457_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1457_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1457_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1457_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1457,"target_cube_count":12,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,0,2],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[1,1,0]],[[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,2,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[3,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[566,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1458","image_path":"images/combination3d_1458.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1458_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1458_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1458_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1458_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1458_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1458,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]]],"total_cube_count":8}],"canvas_size":[602,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1459","image_path":"images/combination3d_1459.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1459_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1459_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1459_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1459_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1459_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1459,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[599,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1460","image_path":"images/combination3d_1460.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1460_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1460_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1460_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1460_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1460_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1460,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[555,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1461","image_path":"images/combination3d_1461.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1461_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1461_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1461_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1461_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1461_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1461,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[3,1,0],[4,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,3,2],[2,1,1],[2,2,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1],[1,2,4]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[583,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1462","image_path":"images/combination3d_1462.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1462_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1462_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1462_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1462_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_1462_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1462,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[597,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1463","image_path":"images/combination3d_1463.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1463_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1463_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1463_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1463_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1463_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1463,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[590,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1464","image_path":"images/combination3d_1464.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1464_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1464_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1464_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1464_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1464_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1464,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[0,2,1],[0,2,2],[0,3,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[580,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1465","image_path":"images/combination3d_1465.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1465_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1465_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1465_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1465_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1465_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1465,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[596,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1466","image_path":"images/combination3d_1466.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1466_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1466_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1466_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1466_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1466_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1466,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[592,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1467","image_path":"images/combination3d_1467.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1467_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1467_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1467_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_1467_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1467_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1467,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,0,3],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,1,3],[1,2,4],[2,2,4]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[0,3,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,4,0],[2,4,1],[2,4,2]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[0,3,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1],[2,4,2]]],"total_cube_count":14}],"canvas_size":[572,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1468","image_path":"images/combination3d_1468.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1468_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1468_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1468_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1468_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1468_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1468,"target_cube_count":14,"target_cubes":[[0,2,0],[0,3,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1],[2,4,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,2],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,1,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[556,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1469","image_path":"images/combination3d_1469.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1469_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1469_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1469_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1469_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1469_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1469,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,2,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,1,0]],[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[2,1,2],[3,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,1,0]],[[0,2,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]]],"total_cube_count":14}],"canvas_size":[600,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1470","image_path":"images/combination3d_1470.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1470_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1470_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1470_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1470_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1470_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1470,"target_cube_count":13,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[568,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1471","image_path":"images/combination3d_1471.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1471_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1471_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1471_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1471_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1471_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1471,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,1,1],[1,1,2],[1,2,1],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[578,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1472","image_path":"images/combination3d_1472.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1472_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1472_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1472_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1472_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1472_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1472,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14}],"canvas_size":[562,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1473","image_path":"images/combination3d_1473.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1473_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1473_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1473_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1473_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1473_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1473,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,1]]],"total_cube_count":15}],"canvas_size":[557,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1474","image_path":"images/combination3d_1474.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1474_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1474_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1474_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1474_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1474_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1474,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,3]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":13}],"canvas_size":[564,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1475","image_path":"images/combination3d_1475.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1475_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1475_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1475_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1475_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1475_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1475,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[1,1,1],[1,1,2],[2,1,0],[2,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":9}],"canvas_size":[620,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1476","image_path":"images/combination3d_1476.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1476_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1476_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1476_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1476_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1476_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1476,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,2],[1,2,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11}],"canvas_size":[612,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1477","image_path":"images/combination3d_1477.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1477_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1477_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1477_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1477_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1477_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1477,"target_cube_count":11,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,3],[1,1,2],[1,1,3],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[3,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2]],[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,2]]],"total_cube_count":13}],"canvas_size":[572,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1478","image_path":"images/combination3d_1478.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1478_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1478_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1478_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1478_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1478_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1478,"target_cube_count":13,"target_cubes":[[0,3,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[3,1,0],[3,1,1],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,1,2],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":10}],"canvas_size":[556,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1479","image_path":"images/combination3d_1479.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1479_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1479_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1479_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1479_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1479_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1479,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,2],[2,1,1],[2,1,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":12}],"canvas_size":[562,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1480","image_path":"images/combination3d_1480.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1480_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1480_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1480_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1480_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1480_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1480,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[0,3,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[1,3,2],[2,0,1],[2,2,1],[2,3,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":14}],"canvas_size":[552,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1481","image_path":"images/combination3d_1481.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1481_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1481_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1481_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1481_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1481_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1481,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[560,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1482","image_path":"images/combination3d_1482.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1482_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1482_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1482_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1482_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1482_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1482,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[0,4,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,3,1],[1,0,3],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,1],[0,3,2],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[2,0,1],[2,1,1],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[567,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1483","image_path":"images/combination3d_1483.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1483_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1483_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1483_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1483_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1483_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1483,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[568,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1484","image_path":"images/combination3d_1484.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1484_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1484_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1484_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1484_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1484_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1484,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[1,0,1],[1,1,1],[1,3,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2]]],"total_cube_count":13}],"canvas_size":[595,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1485","image_path":"images/combination3d_1485.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1485_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1485_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1485_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_1485_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1485_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1485,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,2],[1,2,1],[1,2,2],[2,1,2],[2,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[605,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1486","image_path":"images/combination3d_1486.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1486_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1486_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1486_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1486_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1486_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1486,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,2,1],[1,3,1],[2,3,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[2,0,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[572,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1487","image_path":"images/combination3d_1487.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1487_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1487_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1487_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1487_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1487_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1487,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,2,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9}],"canvas_size":[585,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1488","image_path":"images/combination3d_1488.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1488_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1488_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1488_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1488_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1488_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1488,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[604,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1489","image_path":"images/combination3d_1489.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1489_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1489_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1489_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1489_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1489_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1489,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":8}],"canvas_size":[616,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1490","image_path":"images/combination3d_1490.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1490_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1490_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1490_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1490_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1490_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1490,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[578,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1491","image_path":"images/combination3d_1491.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1491_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1491_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1491_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1491_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1491_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1491,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[1,3,3]],[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2]],[[0,0,2],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,1,2],[2,2,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,2],[2,1,2],[3,1,2]],[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":14}],"canvas_size":[567,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1492","image_path":"images/combination3d_1492.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1492_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1492_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1492_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1492_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1492_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1492,"target_cube_count":14,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[2,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[576,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1493","image_path":"images/combination3d_1493.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1493_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1493_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1493_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1493_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1493_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1493,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,3,0],[1,3,1],[1,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,1,1],[1,2,1],[2,0,1],[2,0,2],[2,1,1],[3,0,2]]],"total_cube_count":10}],"canvas_size":[572,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1494","image_path":"images/combination3d_1494.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1494_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1494_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1494_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1494_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1494_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1494,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,1],[2,2,1]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[604,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1495","image_path":"images/combination3d_1495.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1495_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1495_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1495_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1495_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1495_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1495,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[4,0,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,1,1],[2,1,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[559,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1496","image_path":"images/combination3d_1496.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1496_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1496_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1496_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1496_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1496_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1496,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,2,2],[0,3,2]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[560,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1497","image_path":"images/combination3d_1497.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1497_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1497_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1497_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1497_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1497_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1497,"target_cube_count":10,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":8}],"canvas_size":[569,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1498","image_path":"images/combination3d_1498.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1498_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1498_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1498_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1498_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1498_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1498,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[2,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,1],[1,1,2],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":10}],"canvas_size":[595,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1499","image_path":"images/combination3d_1499.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1499_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1499_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1499_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1499_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1499_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1499,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,2],[1,1,2],[1,1,3],[2,0,1],[2,0,2],[3,0,2],[4,0,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,0,1],[2,1,1],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,1,1],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":14}],"canvas_size":[589,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1500","image_path":"images/combination3d_1500.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1500_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1500_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1500_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1500_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1500_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1500,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":9}],"canvas_size":[578,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1501","image_path":"images/combination3d_1501.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1501_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1501_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1501_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1501_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1501_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1501,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[0,3,2],[1,0,0],[1,0,1],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,3],[1,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,1,1]]],"total_cube_count":12}],"canvas_size":[571,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1502","image_path":"images/combination3d_1502.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1502_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1502_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1502_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1502_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1502_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1502,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,1]]],"total_cube_count":9}],"canvas_size":[609,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1503","image_path":"images/combination3d_1503.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1503_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1503_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1503_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1503_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1503_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1503,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0]],[[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[3,0,1],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]],[[0,2,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]],[[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[603,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1504","image_path":"images/combination3d_1504.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1504_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1504_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1504_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1504_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1504_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1504,"target_cube_count":14,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[2,3,3],[2,3,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9}],"canvas_size":[565,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1505","image_path":"images/combination3d_1505.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1505_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1505_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1505_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_1505_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1505_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1505,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,3,0],[2,3,0],[3,3,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,1,2],[1,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[573,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1506","image_path":"images/combination3d_1506.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1506_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1506_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1506_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1506_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1506_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1506,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[3,0,1],[3,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[555,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1507","image_path":"images/combination3d_1507.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1507_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1507_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1507_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1507_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1507_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1507,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12}],"canvas_size":[589,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1508","image_path":"images/combination3d_1508.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1508_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1508_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1508_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1508_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1508_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1508,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,2]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[585,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1509","image_path":"images/combination3d_1509.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1509_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1509_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1509_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1509_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1509_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1509,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,1],[2,2,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]]],"total_cube_count":11}],"canvas_size":[601,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1510","image_path":"images/combination3d_1510.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1510_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1510_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1510_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1510_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1510_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1510,"target_cube_count":11,"target_cubes":[[0,3,0],[0,3,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[3,0,0],[3,1,0],[4,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[3,0,0],[3,1,0],[4,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,3],[0,1,4],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[573,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1511","image_path":"images/combination3d_1511.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1511_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1511_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1511_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1511_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1511_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1511,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[610,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1512","image_path":"images/combination3d_1512.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1512_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1512_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1512_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1512_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1512_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1512,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[619,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1513","image_path":"images/combination3d_1513.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1513_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1513_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1513_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_1513_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1513_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1513,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,4,1],[1,3,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,3,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,1],[2,1,2],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[1,1,1],[1,3,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[550,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1514","image_path":"images/combination3d_1514.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1514_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1514_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1514_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1514_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1514_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1514,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[0,4,2],[1,3,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":12}],"canvas_size":[590,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1515","image_path":"images/combination3d_1515.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1515_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1515_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1515_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1515_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1515_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1515,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[579,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1516","image_path":"images/combination3d_1516.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1516_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1516_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1516_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1516_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1516_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1516,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":8}],"canvas_size":[600,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1517","image_path":"images/combination3d_1517.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1517_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1517_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1517_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1517_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1517_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1517,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,1,2]],[[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,0]],[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,0]],[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,1,1]]],"total_cube_count":13}],"canvas_size":[575,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1518","image_path":"images/combination3d_1518.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1518_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1518_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1518_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1518_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1518_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1518,"target_cube_count":13,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[1,1,1],[1,1,2],[2,0,2],[2,1,2],[3,1,2]]],"total_cube_count":14}],"canvas_size":[581,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1519","image_path":"images/combination3d_1519.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1519_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1519_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1519_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1519_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1519_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1519,"target_cube_count":14,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,1],[2,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":9}],"canvas_size":[602,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1520","image_path":"images/combination3d_1520.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1520_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1520_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1520_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1520_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1520_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1520,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[4,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0],[4,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,2],[2,1,2],[3,0,0],[3,1,0],[3,1,1],[3,1,2],[4,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[550,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1521","image_path":"images/combination3d_1521.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1521_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1521_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1521_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1521_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1521_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1521,"target_cube_count":10,"target_cubes":[[0,2,0],[1,2,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[4,2,0],[4,3,0],[4,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,0,3],[2,1,2],[2,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,1],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[572,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1522","image_path":"images/combination3d_1522.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1522_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1522_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1522_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1522_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1522_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1522,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[0,1,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,2,1],[2,3,1]]],"total_cube_count":13}],"canvas_size":[572,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1523","image_path":"images/combination3d_1523.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1523_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1523_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1523_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_1523_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1523_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1523,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,2,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0]]],"total_cube_count":9}],"canvas_size":[556,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1524","image_path":"images/combination3d_1524.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1524_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1524_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1524_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1524_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1524_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1524,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":13}],"canvas_size":[588,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1525","image_path":"images/combination3d_1525.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1525_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1525_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1525_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1525_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1525_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1525,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[579,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1526","image_path":"images/combination3d_1526.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1526_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1526_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1526_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1526_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1526_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1526,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[1,0,2],[1,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,1,2],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11}],"canvas_size":[618,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1527","image_path":"images/combination3d_1527.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1527_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1527_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1527_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1527_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1527_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1527,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1],[3,0,0],[3,0,1],[3,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9}],"canvas_size":[595,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1528","image_path":"images/combination3d_1528.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1528_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1528_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1528_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1528_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1528_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1528,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,1],[2,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,1,2],[0,1,3],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[592,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1529","image_path":"images/combination3d_1529.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1529_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1529_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1529_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1529_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1529_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1529,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,2],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[554,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1530","image_path":"images/combination3d_1530.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1530_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1530_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1530_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1530_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1530_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1530,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,3],[0,2,1],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12}],"canvas_size":[554,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1531","image_path":"images/combination3d_1531.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1531_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1531_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1531_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1531_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1531_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1531,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":10}],"canvas_size":[572,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1532","image_path":"images/combination3d_1532.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1532_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1532_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1532_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1532_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1532_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1532,"target_cube_count":10,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":10}],"canvas_size":[574,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1533","image_path":"images/combination3d_1533.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1533_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1533_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1533_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1533_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1533_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1533,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[594,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1534","image_path":"images/combination3d_1534.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1534_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1534_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1534_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1534_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1534_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1534,"target_cube_count":9,"target_cubes":[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[589,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1535","image_path":"images/combination3d_1535.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1535_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1535_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1535_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1535_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1535_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1535,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,2,1],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[564,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1536","image_path":"images/combination3d_1536.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1536_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1536_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1536_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1536_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1536_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1536,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,1,1],[2,1,2],[2,1,3],[3,0,1],[3,0,2],[3,1,0],[3,1,1],[3,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[1,2,1],[1,3,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11}],"canvas_size":[594,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1537","image_path":"images/combination3d_1537.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1537_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1537_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1537_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1537_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1537_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1537,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,0,0],[3,0,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,1],[1,0,2],[1,1,2],[1,2,1],[1,3,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,2,1],[2,2,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[585,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1538","image_path":"images/combination3d_1538.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1538_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1538_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1538_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1538_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_1538_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1538,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[552,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1539","image_path":"images/combination3d_1539.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1539_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1539_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1539_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1539_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1539_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1539,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,2],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12}],"canvas_size":[554,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1540","image_path":"images/combination3d_1540.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1540_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1540_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1540_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1540_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1540_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1540,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":10}],"canvas_size":[591,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1541","image_path":"images/combination3d_1541.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1541_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1541_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1541_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_1541_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1541_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1541,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[2,2,0],[2,2,1],[2,2,2],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[3,3,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[3,0,1],[3,1,1],[3,2,1],[3,2,2],[3,3,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,3],[1,0,2],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,3],[3,2,3]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13}],"canvas_size":[597,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1542","image_path":"images/combination3d_1542.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1542_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1542_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1542_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1542_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1542_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1542,"target_cube_count":13,"target_cubes":[[0,2,0],[1,2,0],[2,2,0],[2,2,1],[2,2,2],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[3,3,0],[4,1,0],[4,2,0],[5,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[562,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1543","image_path":"images/combination3d_1543.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1543_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1543_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1543_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1543_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1543_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1543,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[4,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,2,0],[3,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,2],[1,1,1],[1,2,0],[1,3,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,2,0],[3,2,1]]],"total_cube_count":13}],"canvas_size":[574,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1544","image_path":"images/combination3d_1544.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1544_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1544_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1544_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1544_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1544_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1544,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[575,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1545","image_path":"images/combination3d_1545.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1545_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1545_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1545_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_1545_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1545_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1545,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,2,1],[1,2,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":10}],"canvas_size":[567,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1546","image_path":"images/combination3d_1546.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1546_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1546_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1546_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1546_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1546_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1546,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[564,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1547","image_path":"images/combination3d_1547.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1547_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1547_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1547_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1547_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_1547_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1547,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,2],[0,1,2],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[570,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1548","image_path":"images/combination3d_1548.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1548_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1548_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1548_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_1548_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1548_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1548,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[4,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12}],"canvas_size":[615,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1549","image_path":"images/combination3d_1549.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1549_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1549_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1549_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1549_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1549_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1549,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,1],[0,2,2],[0,3,1],[0,3,2],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[559,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1550","image_path":"images/combination3d_1550.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1550_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1550_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1550_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1550_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1550_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1550,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":12}],"canvas_size":[620,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1551","image_path":"images/combination3d_1551.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1551_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1551_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1551_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1551_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1551_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1551,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[571,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1552","image_path":"images/combination3d_1552.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1552_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1552_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1552_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1552_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1552_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1552,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8}],"canvas_size":[588,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1553","image_path":"images/combination3d_1553.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1553_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1553_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1553_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1553_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1553_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1553,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,1],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[603,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1554","image_path":"images/combination3d_1554.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1554_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1554_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1554_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1554_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1554_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1554,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":8}],"canvas_size":[594,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1555","image_path":"images/combination3d_1555.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1555_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1555_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1555_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1555_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1555_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1555,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,2,0],[4,2,0],[4,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,4,0],[1,4,0],[2,0,1],[2,1,1],[2,2,1],[2,3,0],[2,3,1],[2,4,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,4],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]]],"total_cube_count":12}],"canvas_size":[594,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1556","image_path":"images/combination3d_1556.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1556_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1556_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1556_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,5","question_id":"combination3d_1556_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1556_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1556,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[559,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1557","image_path":"images/combination3d_1557.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1557_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1557_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1557_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1557_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1557_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1557,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,2],[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[569,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1558","image_path":"images/combination3d_1558.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1558_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1558_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1558_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1558_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1558_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1558,"target_cube_count":10,"target_cubes":[[0,4,0],[0,5,0],[0,5,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[1,5,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,2]]],"total_cube_count":10}],"canvas_size":[608,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1559","image_path":"images/combination3d_1559.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1559_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1559_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1559_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_1559_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1559_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1559,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[608,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1560","image_path":"images/combination3d_1560.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1560_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1560_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1560_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1560_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1560_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1560,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2]],[[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0],[3,2,1],[4,0,0],[4,1,0],[4,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15}],"canvas_size":[581,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1561","image_path":"images/combination3d_1561.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1561_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1561_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1561_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1561_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1561_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1561,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[2,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":11}],"canvas_size":[594,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1562","image_path":"images/combination3d_1562.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1562_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1562_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1562_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1562_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1562_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1562,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[590,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1563","image_path":"images/combination3d_1563.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1563_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1563_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1563_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1563_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1563_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1563,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[562,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1564","image_path":"images/combination3d_1564.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1564_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1564_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1564_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1564_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1564_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1564,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]]],"total_cube_count":12}],"canvas_size":[588,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1565","image_path":"images/combination3d_1565.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1565_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1565_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1565_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1565_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1565_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1565,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,1,2],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1]],[[0,0,1],[0,0,2],[0,1,1],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":15}],"canvas_size":[558,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1566","image_path":"images/combination3d_1566.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1566_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1566_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1566_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1566_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1566_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1566,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,0],[2,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[565,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1567","image_path":"images/combination3d_1567.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1567_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1567_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1567_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1567_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1567_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1567,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,2],[1,1,2],[1,1,3]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,4,1],[2,0,0],[2,1,0],[2,3,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13}],"canvas_size":[608,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1568","image_path":"images/combination3d_1568.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1568_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1568_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1568_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_1568_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1568_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1568,"target_cube_count":13,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[599,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1569","image_path":"images/combination3d_1569.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1569_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1569_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1569_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1569_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1569_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1569,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2]]],"total_cube_count":12}],"canvas_size":[559,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1570","image_path":"images/combination3d_1570.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1570_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1570_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1570_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1570_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1570_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1570,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[572,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1571","image_path":"images/combination3d_1571.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1571_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1571_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1571_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1571_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1571_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1571,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[4,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[585,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1572","image_path":"images/combination3d_1572.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1572_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1572_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1572_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1572_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1572_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1572,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[599,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1573","image_path":"images/combination3d_1573.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1573_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1573_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1573_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1573_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1573_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1573,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[611,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1574","image_path":"images/combination3d_1574.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1574_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1574_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1574_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1574_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1574_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1574,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[578,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1575","image_path":"images/combination3d_1575.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1575_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1575_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1575_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1575_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1575_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1575,"target_cube_count":9,"target_cubes":[[0,3,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,1],[3,1,1],[3,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,1],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[589,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1576","image_path":"images/combination3d_1576.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1576_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1576_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1576_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1576_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1576_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1576,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11}],"canvas_size":[587,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1577","image_path":"images/combination3d_1577.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1577_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1577_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1577_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1577_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_1577_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1577,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,2],[1,2,3],[2,1,1],[2,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":15}],"canvas_size":[607,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1578","image_path":"images/combination3d_1578.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1578_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1578_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1578_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1578_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1578_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1578,"target_cube_count":14,"target_cubes":[[0,3,0],[0,3,1],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[3,0,0],[3,0,1],[3,3,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[565,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1579","image_path":"images/combination3d_1579.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1579_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1579_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1579_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1579_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1579_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1579,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[566,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1580","image_path":"images/combination3d_1580.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1580_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1580_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1580_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1580_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1580_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1580,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,2,0],[2,2,1]]],"total_cube_count":12}],"canvas_size":[595,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1581","image_path":"images/combination3d_1581.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1581_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1581_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1581_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1581_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1581_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1581,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[3,0,0],[4,0,0],[4,0,1],[4,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[576,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1582","image_path":"images/combination3d_1582.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1582_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1582_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1582_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1582_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1582_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1582,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,2,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,3,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[3,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[3,0,1],[3,1,1]]],"total_cube_count":15}],"canvas_size":[604,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1583","image_path":"images/combination3d_1583.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1583_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1583_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1583_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_1583_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1583_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1583,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,1],[0,1,2],[0,2,1],[0,3,0],[0,3,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":13}],"canvas_size":[592,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1584","image_path":"images/combination3d_1584.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1584_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1584_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1584_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1584_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1584_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1584,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":14}],"canvas_size":[590,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1585","image_path":"images/combination3d_1585.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1585_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1585_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1585_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1585_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_1585_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1585,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,3,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,2,1],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[597,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1586","image_path":"images/combination3d_1586.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1586_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1586_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1586_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1586_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1586_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1586,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,2]]],"total_cube_count":12}],"canvas_size":[560,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1587","image_path":"images/combination3d_1587.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1587_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1587_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1587_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1587_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1587_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1587,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,1],[1,3,2],[2,3,2]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,1]]],"total_cube_count":13}],"canvas_size":[568,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1588","image_path":"images/combination3d_1588.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1588_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1588_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1588_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1588_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1588_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1588,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,1],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[556,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1589","image_path":"images/combination3d_1589.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1589_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1589_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1589_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1589_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1589_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1589,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[4,0,0],[5,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[4,0,0],[5,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[4,0,0],[5,0,0]]],"total_cube_count":14}],"canvas_size":[555,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1590","image_path":"images/combination3d_1590.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1590_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1590_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1590_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1590_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1590_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1590,"target_cube_count":13,"target_cubes":[[0,3,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1],[2,4,0],[2,4,1],[3,3,0],[4,3,0],[5,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,1],[1,0,2],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[570,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1591","image_path":"images/combination3d_1591.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1591_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1591_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1591_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1591_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1591_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1591,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[597,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1592","image_path":"images/combination3d_1592.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1592_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1592_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1592_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_1592_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1592_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1592,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,2,2],[1,0,2],[1,1,2],[1,2,2],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,1],[3,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[605,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1593","image_path":"images/combination3d_1593.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1593_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1593_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1593_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1593_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1593_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1593,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,0,2],[3,0,3],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,1]],[[0,2,0],[0,2,1],[0,3,1],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1]]],"total_cube_count":14}],"canvas_size":[619,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1594","image_path":"images/combination3d_1594.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1594_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1594_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1594_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1594_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1594_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1594,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[581,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1595","image_path":"images/combination3d_1595.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1595_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1595_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1595_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1595_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1595_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1595,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[4,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12}],"canvas_size":[564,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1596","image_path":"images/combination3d_1596.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1596_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1596_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1596_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1596_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1596_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1596,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[4,0,0],[4,1,0],[4,1,1],[4,2,0],[4,2,1],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]]],"total_cube_count":11}],"canvas_size":[614,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1597","image_path":"images/combination3d_1597.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1597_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1597_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1597_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1597_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1597_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1597,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[2,0,0],[2,1,0],[2,2,0],[2,4,0],[2,5,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,2],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14}],"canvas_size":[610,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1598","image_path":"images/combination3d_1598.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1598_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1598_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1598_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1598_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1598_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1598,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[618,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1599","image_path":"images/combination3d_1599.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1599_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1599_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1599_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1599_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1599_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1599,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":12}],"canvas_size":[551,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1600","image_path":"images/combination3d_1600.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1600_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1600_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1600_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1600_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_1600_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1600,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[1,0,1],[1,0,2],[1,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[1,2,2],[2,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":14}],"canvas_size":[600,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1601","image_path":"images/combination3d_1601.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1601_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1601_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1601_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1601_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1601_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1601,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,2]]],"total_cube_count":11}],"canvas_size":[584,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1602","image_path":"images/combination3d_1602.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1602_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1602_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1602_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1602_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1602_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1602,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[616,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1603","image_path":"images/combination3d_1603.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1603_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1603_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1603_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1603_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1603_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1603,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,1],[2,0,1],[2,1,1],[2,2,1],[2,2,2],[3,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,0,2],[2,1,2],[2,2,1],[3,2,0],[3,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[553,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1604","image_path":"images/combination3d_1604.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1604_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1604_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1604_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1604_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1604_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1604,"target_cube_count":14,"target_cubes":[[0,0,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[567,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1605","image_path":"images/combination3d_1605.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1605_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1605_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1605_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1605_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1605_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1605,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]]],"total_cube_count":11}],"canvas_size":[616,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1606","image_path":"images/combination3d_1606.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1606_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1606_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1606_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1606_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1606_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1606,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0],[3,3,0],[3,3,1],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,1],[1,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11}],"canvas_size":[565,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1607","image_path":"images/combination3d_1607.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1607_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1607_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1607_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1607_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1607_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1607,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[573,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1608","image_path":"images/combination3d_1608.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1608_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1608_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1608_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1608_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1608_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1608,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[605,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1609","image_path":"images/combination3d_1609.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1609_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1609_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1609_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1609_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1609_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1609,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[587,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1610","image_path":"images/combination3d_1610.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1610_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1610_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1610_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1610_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1610_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1610,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":12}],"canvas_size":[586,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1611","image_path":"images/combination3d_1611.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1611_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1611_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1611_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1611_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1611_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1611,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,0,2],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,2],[1,0,3],[1,1,2],[1,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":14}],"canvas_size":[569,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1612","image_path":"images/combination3d_1612.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1612_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1612_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1612_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1612_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1612_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1612,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,1,2],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":8}],"canvas_size":[593,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1613","image_path":"images/combination3d_1613.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1613_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1613_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1613_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1613_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1613_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1613,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":9}],"canvas_size":[575,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1614","image_path":"images/combination3d_1614.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1614_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1614_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1614_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1614_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1614_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1614,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,2,3]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,2,3]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[595,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1615","image_path":"images/combination3d_1615.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1615_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1615_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1615_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1615_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1615_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1615,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[596,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1616","image_path":"images/combination3d_1616.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1616_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1616_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1616_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1616_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1616_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1616,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,2,3],[1,2,4],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":13}],"canvas_size":[612,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1617","image_path":"images/combination3d_1617.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1617_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1617_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1617_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1617_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1617_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1617,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":12}],"canvas_size":[560,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1618","image_path":"images/combination3d_1618.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1618_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1618_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1618_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1618_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1618_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1618,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[556,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1619","image_path":"images/combination3d_1619.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1619_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1619_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1619_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1619_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1619_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1619,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":8}],"canvas_size":[560,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1620","image_path":"images/combination3d_1620.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1620_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1620_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1620_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1620_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1620_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1620,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,3,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1]]],"total_cube_count":13}],"canvas_size":[570,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1621","image_path":"images/combination3d_1621.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1621_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1621_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1621_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1621_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1621_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1621,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[1,0,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[607,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1622","image_path":"images/combination3d_1622.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1622_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1622_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1622_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1622_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1622_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1622,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,4],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,4],[2,1,0],[2,1,1],[2,2,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[567,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1623","image_path":"images/combination3d_1623.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1623_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1623_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1623_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1623_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1623_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1623,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[581,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1624","image_path":"images/combination3d_1624.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1624_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1624_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1624_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1624_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1624_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1624,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1]]],"total_cube_count":14}],"canvas_size":[591,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1625","image_path":"images/combination3d_1625.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1625_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1625_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1625_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1625_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1625_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1625,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10}],"canvas_size":[590,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1626","image_path":"images/combination3d_1626.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1626_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1626_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1626_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1626_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1626_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1626,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11}],"canvas_size":[595,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1627","image_path":"images/combination3d_1627.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1627_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1627_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1627_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1627_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1627_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1627,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[0,3,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[563,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1628","image_path":"images/combination3d_1628.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1628_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1628_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1628_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1628_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1628_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1628,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[607,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1629","image_path":"images/combination3d_1629.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1629_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1629_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1629_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1629_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1629_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1629,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[1,4,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[1,3,1],[1,4,1],[1,4,2]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[556,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1630","image_path":"images/combination3d_1630.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1630_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1630_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1630_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1630_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1630_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1630,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[1,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,1],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[557,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1631","image_path":"images/combination3d_1631.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1631_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1631_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1631_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1631_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1631_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1631,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[575,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1632","image_path":"images/combination3d_1632.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1632_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1632_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1632_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1632_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1632_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1632,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1]],[[0,0,2],[0,1,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,2,1],[2,0,1],[2,2,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[619,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1633","image_path":"images/combination3d_1633.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1633_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1633_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1633_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1633_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1633_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1633,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[3,1,0],[3,1,1],[3,1,2],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1]]],"total_cube_count":8}],"canvas_size":[562,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1634","image_path":"images/combination3d_1634.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1634_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1634_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1634_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1634_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1634_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1634,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[558,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1635","image_path":"images/combination3d_1635.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1635_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1635_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1635_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1635_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1635_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1635,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[566,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1636","image_path":"images/combination3d_1636.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1636_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1636_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1636_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1636_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,5","question_id":"combination3d_1636_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1636,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":9}],"canvas_size":[591,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1637","image_path":"images/combination3d_1637.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1637_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1637_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1637_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1637_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1637_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1637,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,1,0],[1,3,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,3],[1,0,0],[1,0,3],[1,1,3],[2,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[3,0,0],[4,0,0],[4,0,1],[4,0,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,3],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,1],[2,1,2],[2,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[3,0,0],[3,1,0],[4,0,0],[4,0,1],[4,0,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[608,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1638","image_path":"images/combination3d_1638.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1638_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1638_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1638_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1638_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1638_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1638,"target_cube_count":13,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[3,1,0],[4,1,0],[4,1,1],[4,1,2],[5,0,0],[5,1,0],[6,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,3,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[1,3,1],[2,2,1],[2,3,1],[2,3,2]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[0,2,3],[1,1,0],[1,1,1],[1,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[559,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1639","image_path":"images/combination3d_1639.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1639_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1639_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1639_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_1639_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1639_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1639,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,1,5],[1,1,0],[1,1,4]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[3,1,0],[3,1,1],[4,0,0],[4,1,0],[4,1,1],[5,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[3,1,0],[4,0,0],[4,1,0],[4,1,1],[5,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[615,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1640","image_path":"images/combination3d_1640.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1640_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1640_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1640_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1640_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1640_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1640,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[3,1,0],[4,0,0],[4,0,1],[4,0,2],[4,1,0],[4,1,1],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[3,2,0],[3,2,1],[3,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[2,4,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[0,3,2],[0,3,3],[1,1,1],[1,3,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[3,2,0],[3,2,1],[3,3,0],[4,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[597,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1641","image_path":"images/combination3d_1641.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1641_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1641_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1641_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_1641_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1641_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1641,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10}],"canvas_size":[601,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1642","image_path":"images/combination3d_1642.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1642_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1642_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1642_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1642_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1642_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1642,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,1],[0,2,2],[0,2,3],[1,2,0],[1,2,1],[1,3,1],[1,4,1],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,1,2],[2,1,2],[3,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[2,2,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14}],"canvas_size":[591,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1643","image_path":"images/combination3d_1643.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1643_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1643_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1643_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1643_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1643_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1643,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,2],[0,1,2],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,1],[2,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,0],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,1],[1,4,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[607,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1644","image_path":"images/combination3d_1644.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1644_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1644_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1644_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1644_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1644_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1644,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":10}],"canvas_size":[582,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1645","image_path":"images/combination3d_1645.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1645_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1645_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1645_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1645_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1645_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1645,"target_cube_count":10,"target_cubes":[[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[602,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1646","image_path":"images/combination3d_1646.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1646_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1646_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1646_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1646_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1646_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1646,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1]]],"total_cube_count":10}],"canvas_size":[607,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1647","image_path":"images/combination3d_1647.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1647_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1647_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1647_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1647_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_1647_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1647,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0],[2,1,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[551,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1648","image_path":"images/combination3d_1648.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1648_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1648_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1648_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1648_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1648_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1648,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[3,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[605,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1649","image_path":"images/combination3d_1649.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1649_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1649_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1649_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1649_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1649_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1649,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0]]],"total_cube_count":10}],"canvas_size":[611,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1650","image_path":"images/combination3d_1650.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1650_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1650_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1650_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1650_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1650_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1650,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[550,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1651","image_path":"images/combination3d_1651.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1651_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1651_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1651_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_1651_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1651_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1651,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,2],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[595,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1652","image_path":"images/combination3d_1652.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1652_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1652_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1652_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1652_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1652_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1652,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[556,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1653","image_path":"images/combination3d_1653.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1653_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1653_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1653_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_1653_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1653_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1653,"target_cube_count":8,"target_cubes":[[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[581,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1654","image_path":"images/combination3d_1654.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1654_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1654_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1654_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1654_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1654_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1654,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9}],"canvas_size":[614,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1655","image_path":"images/combination3d_1655.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1655_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1655_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1655_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1655_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1655_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1655,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,2,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2]],[[0,0,0],[0,1,0]],[[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":12}],"canvas_size":[612,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1656","image_path":"images/combination3d_1656.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1656_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1656_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1656_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1656_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1656_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1656,"target_cube_count":12,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,1],[2,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,0,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,1,2],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[608,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1657","image_path":"images/combination3d_1657.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1657_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1657_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1657_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1657_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1657_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1657,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,2]]],"total_cube_count":10}],"canvas_size":[607,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1658","image_path":"images/combination3d_1658.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1658_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1658_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1658_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1658_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1658_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1658,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14}],"canvas_size":[606,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1659","image_path":"images/combination3d_1659.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1659_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1659_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1659_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_1659_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1659_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1659,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[0,3,4],[1,2,0],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[565,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1660","image_path":"images/combination3d_1660.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1660_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1660_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1660_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_1660_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1660_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1660,"target_cube_count":8,"target_cubes":[[0,0,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,0,2]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":14}],"canvas_size":[611,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1661","image_path":"images/combination3d_1661.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1661_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1661_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1661_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_1661_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1661_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1661,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[2,0,0],[2,0,1],[2,1,1],[3,1,1],[3,1,2]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,3,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,0,1],[3,1,1],[3,1,2]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,3,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":15}],"canvas_size":[587,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1662","image_path":"images/combination3d_1662.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1662_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1662_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1662_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1662_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1662_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1662,"target_cube_count":14,"target_cubes":[[0,3,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[565,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1663","image_path":"images/combination3d_1663.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1663_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1663_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1663_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1663_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1663_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1663,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[2,0,0],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[601,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1664","image_path":"images/combination3d_1664.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1664_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1664_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1664_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1664_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1664_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1664,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8}],"canvas_size":[618,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1665","image_path":"images/combination3d_1665.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1665_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1665_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1665_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_1665_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1665_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1665,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[619,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1666","image_path":"images/combination3d_1666.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1666_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1666_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1666_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_1666_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1666_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1666,"target_cube_count":8,"target_cubes":[[0,3,0],[1,0,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,3],[1,1,3]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,2],[1,1,2],[2,1,2]]],"total_cube_count":11}],"canvas_size":[613,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1667","image_path":"images/combination3d_1667.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1667_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1667_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1667_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1667_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1667_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1667,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[562,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1668","image_path":"images/combination3d_1668.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1668_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1668_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1668_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_1668_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1668_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1668,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,2,3]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,2],[2,1,2]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12}],"canvas_size":[579,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1669","image_path":"images/combination3d_1669.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1669_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1669_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1669_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1669_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1669_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1669,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,2,0],[2,3,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,4,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11}],"canvas_size":[603,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1670","image_path":"images/combination3d_1670.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1670_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1670_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1670_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1670_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1670_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1670,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1],[3,1,2],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[586,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1671","image_path":"images/combination3d_1671.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1671_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1671_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1671_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1671_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1671_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1671,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[618,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1672","image_path":"images/combination3d_1672.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1672_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1672_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1672_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1672_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1672_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1672,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":10}],"canvas_size":[588,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1673","image_path":"images/combination3d_1673.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1673_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1673_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1673_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1673_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1673_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1673,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[4,1,0],[4,2,0],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,1],[1,1,2]],[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,3],[1,1,2],[1,2,2],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[594,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1674","image_path":"images/combination3d_1674.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1674_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1674_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1674_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1674_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1674_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1674,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[583,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1675","image_path":"images/combination3d_1675.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1675_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1675_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1675_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1675_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1675_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1675,"target_cube_count":8,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[553,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1676","image_path":"images/combination3d_1676.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1676_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1676_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1676_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1676_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1676_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1676,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[0,2,1],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,1,1],[3,2,0],[3,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0]]],"total_cube_count":15}],"canvas_size":[593,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1677","image_path":"images/combination3d_1677.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1677_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1677_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1677_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1677_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1677_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1677,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":13}],"canvas_size":[583,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1678","image_path":"images/combination3d_1678.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1678_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1678_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1678_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1678_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1678_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1678,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[0,4,2],[1,0,0],[1,0,1],[1,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,2,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,1],[0,1,2],[1,1,2],[1,2,2],[1,3,2],[2,0,0],[2,0,1],[2,0,2],[2,1,2],[2,1,3],[2,2,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":15}],"canvas_size":[561,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1679","image_path":"images/combination3d_1679.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1679_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1679_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1679_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1679_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1679_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1679,"target_cube_count":14,"target_cubes":[[0,2,0],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[587,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1680","image_path":"images/combination3d_1680.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1680_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1680_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1680_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1680_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1680_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1680,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,1,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,2]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":14}],"canvas_size":[584,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1681","image_path":"images/combination3d_1681.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1681_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1681_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1681_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1681_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1681_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1681,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,1,0],[4,0,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,3,2],[2,1,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,1],[1,1,2],[1,2,2],[2,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,1,2]]],"total_cube_count":14}],"canvas_size":[595,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1682","image_path":"images/combination3d_1682.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1682_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1682_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1682_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1682_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1682_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1682,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9}],"canvas_size":[552,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1683","image_path":"images/combination3d_1683.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1683_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1683_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1683_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_1683_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1683_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1683,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1],[1,1,2],[1,2,1]],[[0,1,1],[1,1,1],[2,0,0],[2,0,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12}],"canvas_size":[611,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1684","image_path":"images/combination3d_1684.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1684_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1684_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1684_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1684_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1684_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1684,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,3,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,3,0],[2,3,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":14}],"canvas_size":[620,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1685","image_path":"images/combination3d_1685.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1685_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1685_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1685_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1685_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1685_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1685,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":8}],"canvas_size":[577,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1686","image_path":"images/combination3d_1686.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1686_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1686_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1686_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1686_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1686_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1686,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[603,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1687","image_path":"images/combination3d_1687.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1687_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1687_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1687_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1687_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1687_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1687,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,0,1],[3,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14}],"canvas_size":[588,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1688","image_path":"images/combination3d_1688.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1688_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1688_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1688_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1688_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1688_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1688,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,1,1],[0,1,2],[1,0,1],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[618,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1689","image_path":"images/combination3d_1689.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1689_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1689_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1689_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1689_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1689_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1689,"target_cube_count":10,"target_cubes":[[0,0,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,2,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,2,1],[2,2,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[558,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1690","image_path":"images/combination3d_1690.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1690_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1690_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1690_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1690_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1690_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1690,"target_cube_count":11,"target_cubes":[[0,2,0],[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,1,2],[0,2,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":12}],"canvas_size":[582,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1691","image_path":"images/combination3d_1691.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1691_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1691_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1691_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1691_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1691_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1691,"target_cube_count":12,"target_cubes":[[0,3,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1],[2,4,2],[2,5,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[570,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1692","image_path":"images/combination3d_1692.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1692_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1692_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1692_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1692_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1692_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1692,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0]]],"total_cube_count":12}],"canvas_size":[568,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1693","image_path":"images/combination3d_1693.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1693_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1693_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1693_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1693_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1693_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1693,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,2],[0,0,3],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[554,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1694","image_path":"images/combination3d_1694.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1694_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1694_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1694_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1694_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1694_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1694,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,0,2],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,1,0],[2,0,1]]],"total_cube_count":12}],"canvas_size":[561,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1695","image_path":"images/combination3d_1695.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1695_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1695_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1695_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1695_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1695_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1695,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[553,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1696","image_path":"images/combination3d_1696.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1696_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1696_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1696_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1696_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1696_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1696,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[597,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1697","image_path":"images/combination3d_1697.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1697_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1697_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1697_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_1697_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1697_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1697,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,1,1],[1,2,1],[1,2,2],[2,0,1],[2,1,1],[2,2,1]],[[0,2,1],[0,3,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":14}],"canvas_size":[603,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1698","image_path":"images/combination3d_1698.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1698_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1698_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1698_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1698_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1698_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1698,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2]]],"total_cube_count":9}],"canvas_size":[589,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1699","image_path":"images/combination3d_1699.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1699_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1699_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1699_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_1699_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1699_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1699,"target_cube_count":9,"target_cubes":[[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[605,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1700","image_path":"images/combination3d_1700.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1700_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1700_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1700_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1700_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1700_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1700,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,2],[3,1,0],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,0,1],[1,2,0],[1,3,1],[2,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[612,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1701","image_path":"images/combination3d_1701.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1701_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1701_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1701_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1701_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1701_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1701,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,1,1],[3,1,2],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,1],[2,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[603,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1702","image_path":"images/combination3d_1702.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1702_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1702_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1702_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1702_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1702_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1702,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[616,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1703","image_path":"images/combination3d_1703.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1703_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1703_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1703_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1703_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1703_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1703,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[617,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1704","image_path":"images/combination3d_1704.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1704_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1704_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1704_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1704_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1704_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1704,"target_cube_count":9,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[562,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1705","image_path":"images/combination3d_1705.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1705_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1705_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1705_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1705_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1705_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1705,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[607,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1706","image_path":"images/combination3d_1706.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1706_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1706_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1706_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1706_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1706_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1706,"target_cube_count":11,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,1,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[573,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1707","image_path":"images/combination3d_1707.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1707_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1707_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1707_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_1707_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1707_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1707,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,1],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[590,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1708","image_path":"images/combination3d_1708.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1708_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1708_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1708_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_1708_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1708_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1708,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3]]],"total_cube_count":12}],"canvas_size":[557,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1709","image_path":"images/combination3d_1709.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1709_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1709_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1709_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1709_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1709_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1709,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9}],"canvas_size":[599,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1710","image_path":"images/combination3d_1710.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1710_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1710_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1710_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_1710_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1710_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1710,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,0,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[612,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1711","image_path":"images/combination3d_1711.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1711_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1711_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1711_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1711_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1711_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1711,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[616,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1712","image_path":"images/combination3d_1712.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1712_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1712_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1712_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1712_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1712_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1712,"target_cube_count":9,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[596,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1713","image_path":"images/combination3d_1713.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1713_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1713_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1713_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1713_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1713_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1713,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[603,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1714","image_path":"images/combination3d_1714.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1714_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1714_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1714_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_1714_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1714_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1714,"target_cube_count":8,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,1,0],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":12}],"canvas_size":[615,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1715","image_path":"images/combination3d_1715.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1715_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1715_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1715_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1715_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1715_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1715,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8}],"canvas_size":[551,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1716","image_path":"images/combination3d_1716.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1716_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1716_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1716_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1716_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1716_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1716,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[572,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1717","image_path":"images/combination3d_1717.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1717_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1717_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1717_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1717_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1717_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1717,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]]],"total_cube_count":12}],"canvas_size":[602,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1718","image_path":"images/combination3d_1718.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1718_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1718_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1718_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1718_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1718_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1718,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,3,0],[0,3,1],[1,3,0],[1,3,1],[1,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,2]],[[0,0,0],[1,0,0],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0]]],"total_cube_count":14}],"canvas_size":[614,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1719","image_path":"images/combination3d_1719.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1719_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1719_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1719_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1719_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1719_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1719,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12}],"canvas_size":[588,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1720","image_path":"images/combination3d_1720.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1720_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1720_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1720_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1720_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1720_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1720,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[3,1,0]],[[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[3,1,1]],[[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[3,0,1]],[[0,0,2],[0,1,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,1],[1,1,2],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[2,1,1]]],"total_cube_count":14}],"canvas_size":[566,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1721","image_path":"images/combination3d_1721.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1721_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1721_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1721_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1721_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1721_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1721,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,2,1],[2,2,2],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[611,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1722","image_path":"images/combination3d_1722.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1722_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1722_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1722_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1722_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1722_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1722,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[585,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1723","image_path":"images/combination3d_1723.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1723_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1723_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1723_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1723_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1723_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1723,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,0,1],[3,1,0],[3,1,1],[3,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[3,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[561,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1724","image_path":"images/combination3d_1724.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1724_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1724_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1724_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1724_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1724_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1724,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[1,1,2],[2,0,2],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":9}],"canvas_size":[586,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1725","image_path":"images/combination3d_1725.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1725_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1725_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1725_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1725_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1725_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1725,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0]]],"total_cube_count":12}],"canvas_size":[570,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1726","image_path":"images/combination3d_1726.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1726_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1726_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1726_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1726_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1726_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1726,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,2],[1,1,3],[1,1,4]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,1,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2],[1,2,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13}],"canvas_size":[558,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1727","image_path":"images/combination3d_1727.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1727_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1727_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1727_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1727_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1727_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1727,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[3,0,1],[3,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[1,3,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[598,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1728","image_path":"images/combination3d_1728.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1728_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1728_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1728_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1728_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1728_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1728,"target_cube_count":11,"target_cubes":[[0,4,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[555,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1729","image_path":"images/combination3d_1729.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1729_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1729_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1729_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1729_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1729_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1729,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[574,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1730","image_path":"images/combination3d_1730.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1730_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1730_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1730_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1730_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1730_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1730,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[611,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1731","image_path":"images/combination3d_1731.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1731_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1731_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1731_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1731_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1731_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1731,"target_cube_count":8,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1],[1,1,1],[1,2,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[581,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1732","image_path":"images/combination3d_1732.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1732_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1732_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1732_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1732_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1732_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1732,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,2]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,2]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,1],[4,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,2,0]]],"total_cube_count":12}],"canvas_size":[567,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1733","image_path":"images/combination3d_1733.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1733_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1733_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1733_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1733_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_1733_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1733,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[565,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1734","image_path":"images/combination3d_1734.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1734_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1734_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1734_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1734_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1734_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1734,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,3],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,2],[1,2,3],[2,2,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[0,1,2],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[2,2,0],[2,2,1],[3,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[1,2,0],[1,3,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[1,1,0],[1,2,0],[1,3,0],[2,2,0]]],"total_cube_count":12}],"canvas_size":[604,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1735","image_path":"images/combination3d_1735.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1735_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1735_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1735_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1735_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1735_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1735,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,1],[3,0,1],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[552,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1736","image_path":"images/combination3d_1736.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1736_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1736_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1736_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1736_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1736_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1736,"target_cube_count":10,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[570,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1737","image_path":"images/combination3d_1737.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1737_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1737_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1737_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1737_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1737_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1737,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[0,5,0],[0,5,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[1,1,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[616,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1738","image_path":"images/combination3d_1738.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1738_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1738_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1738_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1738_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1738_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1738,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[580,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1739","image_path":"images/combination3d_1739.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1739_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1739_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1739_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1739_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1739_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1739,"target_cube_count":11,"target_cubes":[[0,0,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,1,2],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[580,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1740","image_path":"images/combination3d_1740.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1740_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1740_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1740_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1740_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_1740_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1740,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,1],[3,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,0,2],[2,0,1],[3,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,2],[1,1,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12}],"canvas_size":[573,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1741","image_path":"images/combination3d_1741.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1741_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1741_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1741_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1741_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1741_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1741,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15}],"canvas_size":[554,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1742","image_path":"images/combination3d_1742.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1742_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1742_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1742_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1742_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1742_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1742,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1],[2,0,2],[2,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[571,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1743","image_path":"images/combination3d_1743.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1743_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1743_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1743_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1743_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1743_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1743,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[1,1,3],[2,1,2],[3,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[589,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1744","image_path":"images/combination3d_1744.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1744_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1744_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1744_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_1744_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1744_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1744,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":13}],"canvas_size":[588,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1745","image_path":"images/combination3d_1745.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1745_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1745_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1745_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1745_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1745_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1745,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,1],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,1],[1,0,2],[1,0,3],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[579,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1746","image_path":"images/combination3d_1746.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1746_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1746_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1746_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1746_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1746_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1746,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[1,1,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[609,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1747","image_path":"images/combination3d_1747.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1747_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1747_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1747_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_1747_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1747_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1747,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,3]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[599,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1748","image_path":"images/combination3d_1748.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1748_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1748_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1748_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1748_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1748_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1748,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,1,2],[4,0,0],[4,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,1],[1,2,1],[2,2,1],[3,0,1],[3,1,0],[3,1,1],[3,2,0],[3,2,1],[4,1,0],[4,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,1,2],[3,2,1],[4,0,0],[4,0,1]]],"total_cube_count":13}],"canvas_size":[581,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1749","image_path":"images/combination3d_1749.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1749_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1749_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1749_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1749_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1749_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1749,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,1,2],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8}],"canvas_size":[597,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1750","image_path":"images/combination3d_1750.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1750_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1750_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1750_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1750_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1750_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1750,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[550,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1751","image_path":"images/combination3d_1751.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1751_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1751_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1751_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1751_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1751_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1751,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[3,0,1],[3,0,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14}],"canvas_size":[577,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1752","image_path":"images/combination3d_1752.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1752_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1752_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1752_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1752_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1752_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1752,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[556,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1753","image_path":"images/combination3d_1753.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1753_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1753_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1753_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1753_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1753_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1753,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[574,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1754","image_path":"images/combination3d_1754.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1754_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1754_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1754_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1754_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1754_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1754,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0],[4,0,0],[4,0,1],[4,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,2,1],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[596,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1755","image_path":"images/combination3d_1755.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1755_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1755_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1755_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1755_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1755_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1755,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":11}],"canvas_size":[586,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1756","image_path":"images/combination3d_1756.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1756_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1756_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1756_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1756_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1756_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1756,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0],[3,2,1],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,0,2],[1,0,1],[2,0,1],[2,1,0],[2,1,1],[2,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,2,0],[0,2,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":15}],"canvas_size":[614,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1757","image_path":"images/combination3d_1757.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1757_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1757_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1757_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1757_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1757_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1757,"target_cube_count":14,"target_cubes":[[0,0,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,1],[0,5,1],[1,1,0],[1,2,1],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,5,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,5,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,2],[2,0,1],[2,1,1],[2,1,2]]],"total_cube_count":14}],"canvas_size":[568,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1758","image_path":"images/combination3d_1758.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1758_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1758_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1758_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1758_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1758_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1758,"target_cube_count":14,"target_cubes":[[0,2,0],[0,3,0],[0,3,1],[0,4,0],[0,5,0],[0,6,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[1,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,1,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,1],[1,1,1],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1],[4,1,1],[4,1,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[606,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1759","image_path":"images/combination3d_1759.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1759_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1759_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1759_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1759_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1759_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1759,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,2],[0,1,3],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[614,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1760","image_path":"images/combination3d_1760.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1760_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1760_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1760_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1760_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1760_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1760,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,3],[0,3,3],[1,2,3],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[561,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1761","image_path":"images/combination3d_1761.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1761_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1761_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1761_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1761_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1761_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1761,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,0,2],[3,1,0],[3,2,0],[3,2,1],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,0,1],[2,2,1],[2,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]],[[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,0],[3,0,1]]],"total_cube_count":15}],"canvas_size":[582,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1762","image_path":"images/combination3d_1762.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1762_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1762_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1762_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1762_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1762_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1762,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11}],"canvas_size":[619,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1763","image_path":"images/combination3d_1763.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1763_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1763_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1763_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1763_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1763_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1763,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[2,1,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0]]],"total_cube_count":10}],"canvas_size":[575,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1764","image_path":"images/combination3d_1764.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1764_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1764_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1764_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1764_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1764_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1764,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1]]],"total_cube_count":9}],"canvas_size":[577,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1765","image_path":"images/combination3d_1765.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1765_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1765_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1765_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1765_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1765_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1765,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1]]],"total_cube_count":11}],"canvas_size":[575,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1766","image_path":"images/combination3d_1766.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1766_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1766_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1766_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1766_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1766_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1766,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,1,0],[3,2,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12}],"canvas_size":[615,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1767","image_path":"images/combination3d_1767.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1767_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1767_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1767_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1767_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1767_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1767,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,0,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[559,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1768","image_path":"images/combination3d_1768.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1768_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1768_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1768_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1768_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1768_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1768,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[553,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1769","image_path":"images/combination3d_1769.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1769_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1769_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1769_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,5","question_id":"combination3d_1769_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1769_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1769,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":12}],"canvas_size":[593,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1770","image_path":"images/combination3d_1770.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1770_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1770_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1770_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1770_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1770_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1770,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":8}],"canvas_size":[571,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1771","image_path":"images/combination3d_1771.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1771_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1771_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1771_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1771_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1771_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1771,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,1,1],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11}],"canvas_size":[575,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1772","image_path":"images/combination3d_1772.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1772_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1772_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1772_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1772_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1772_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1772,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,3,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,3,0],[3,3,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[0,2,3],[1,2,2],[1,2,3],[1,3,3]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,1],[1,0,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":14}],"canvas_size":[603,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1773","image_path":"images/combination3d_1773.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1773_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1773_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1773_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_1773_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1773_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1773,"target_cube_count":14,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,1,0],[3,1,1],[3,2,0],[3,3,0],[3,3,1],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":14}],"canvas_size":[592,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1774","image_path":"images/combination3d_1774.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1774_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1774_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1774_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1774_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1774_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1774,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]]],"total_cube_count":8}],"canvas_size":[598,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1775","image_path":"images/combination3d_1775.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1775_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1775_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1775_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1775_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1775_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1775,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0]],[[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[1,3,3]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[563,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1776","image_path":"images/combination3d_1776.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1776_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1776_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1776_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1776_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1776_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1776,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":14}],"canvas_size":[596,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1777","image_path":"images/combination3d_1777.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1777_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1777_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1777_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1777_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1777_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1777,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,2],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,0,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,2,1],[0,3,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":13}],"canvas_size":[557,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1778","image_path":"images/combination3d_1778.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1778_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1778_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1778_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1778_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1778_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1778,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,1],[1,0,0]],[[0,1,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0]],[[0,1,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,4,0]],[[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[614,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1779","image_path":"images/combination3d_1779.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1779_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1779_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1779_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1779_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1779_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1779,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[616,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1780","image_path":"images/combination3d_1780.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1780_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1780_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1780_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1780_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1780_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1780,"target_cube_count":10,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[560,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1781","image_path":"images/combination3d_1781.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1781_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1781_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1781_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1781_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1781_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1781,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0],[5,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[613,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1782","image_path":"images/combination3d_1782.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1782_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1782_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1782_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1782_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1782_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1782,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[612,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1783","image_path":"images/combination3d_1783.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1783_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1783_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1783_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_1783_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1783_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1783,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,1],[1,1,2]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11}],"canvas_size":[556,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1784","image_path":"images/combination3d_1784.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1784_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1784_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1784_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1784_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1784_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1784,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9}],"canvas_size":[573,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1785","image_path":"images/combination3d_1785.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1785_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1785_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1785_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1785_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1785_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1785,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,1]]],"total_cube_count":9}],"canvas_size":[616,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1786","image_path":"images/combination3d_1786.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1786_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1786_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1786_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1786_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1786_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1786,"target_cube_count":9,"target_cubes":[[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[570,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1787","image_path":"images/combination3d_1787.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1787_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1787_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1787_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1787_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1787_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1787,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[581,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1788","image_path":"images/combination3d_1788.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1788_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1788_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1788_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1788_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1788_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1788,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,3,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,2,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[554,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1789","image_path":"images/combination3d_1789.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1789_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1789_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1789_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1789_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1789_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1789,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,1],[3,1,1]]],"total_cube_count":12}],"canvas_size":[571,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1790","image_path":"images/combination3d_1790.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1790_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1790_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1790_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1790_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1790_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1790,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,3,1],[0,4,0],[0,4,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[595,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1791","image_path":"images/combination3d_1791.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1791_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1791_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1791_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1791_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1791_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1791,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2],[1,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[609,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1792","image_path":"images/combination3d_1792.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1792_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1792_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1792_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1792_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1792_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1792,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":9}],"canvas_size":[553,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1793","image_path":"images/combination3d_1793.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1793_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1793_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1793_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1793_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1793_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1793,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":9}],"canvas_size":[590,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1794","image_path":"images/combination3d_1794.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1794_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1794_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1794_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1794_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1794_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1794,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[563,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1795","image_path":"images/combination3d_1795.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1795_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1795_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1795_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1795_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1795_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1795,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[610,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1796","image_path":"images/combination3d_1796.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1796_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1796_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1796_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1796_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1796_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1796,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[3,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[587,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1797","image_path":"images/combination3d_1797.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1797_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1797_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1797_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1797_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1797_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1797,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[2,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[0,2,2]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,0]]],"total_cube_count":12}],"canvas_size":[611,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1798","image_path":"images/combination3d_1798.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1798_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1798_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1798_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1798_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1798_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1798,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,2,0],[2,2,1],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10}],"canvas_size":[581,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1799","image_path":"images/combination3d_1799.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1799_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1799_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1799_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_1799_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1799_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1799,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[1,2,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[596,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1800","image_path":"images/combination3d_1800.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1800_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1800_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1800_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1800_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1800_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1800,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[563,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1801","image_path":"images/combination3d_1801.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1801_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1801_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1801_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_1801_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1801_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1801,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[3,1,0]]],"total_cube_count":13}],"canvas_size":[619,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1802","image_path":"images/combination3d_1802.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1802_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1802_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1802_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1802_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1802_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1802,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[3,1,0],[3,2,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,1,1],[1,1,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[616,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1803","image_path":"images/combination3d_1803.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1803_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1803_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1803_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1803_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1803_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1803,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[4,0,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[2,0,0],[3,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,0,3],[1,1,1],[1,1,2],[1,1,3],[2,0,1],[2,1,0],[2,1,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[589,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1804","image_path":"images/combination3d_1804.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1804_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1804_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1804_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1804_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1804_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1804,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[3,1,0],[3,2,0],[3,3,0],[4,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],[[0,0,1],[0,1,1],[0,2,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[592,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1805","image_path":"images/combination3d_1805.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1805_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1805_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1805_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1805_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1805_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1805,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":10}],"canvas_size":[558,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1806","image_path":"images/combination3d_1806.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1806_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1806_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1806_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1806_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1806_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1806,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,3,1],[1,3,2]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[3,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,1],[1,3,2]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":13}],"canvas_size":[620,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1807","image_path":"images/combination3d_1807.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1807_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1807_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1807_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1807_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1807_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1807,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,1,2],[3,0,2],[3,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,1],[1,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":13}],"canvas_size":[551,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1808","image_path":"images/combination3d_1808.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1808_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1808_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1808_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_1808_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1808_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1808,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[1,1,2],[1,2,1],[2,1,1],[2,1,2],[2,1,3],[2,2,1],[3,0,1],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[587,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1809","image_path":"images/combination3d_1809.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1809_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1809_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1809_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1809_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1809_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1809,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,1,1],[3,1,2],[3,2,0],[3,2,1],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[559,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1810","image_path":"images/combination3d_1810.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1810_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1810_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1810_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1810_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1810_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1810,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1],[2,1,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,1],[1,1,0],[1,2,1],[2,2,1]]],"total_cube_count":14}],"canvas_size":[620,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1811","image_path":"images/combination3d_1811.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1811_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1811_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1811_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1811_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1811_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1811,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,2],[0,3,1],[0,3,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[594,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1812","image_path":"images/combination3d_1812.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1812_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1812_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1812_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_1812_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1812_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1812,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,1,0],[2,1,1],[2,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[611,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1813","image_path":"images/combination3d_1813.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1813_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1813_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1813_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1813_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1813_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1813,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,2,1],[2,2,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,2],[0,1,3],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[1,2,0],[1,2,2],[1,3,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14}],"canvas_size":[578,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1814","image_path":"images/combination3d_1814.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1814_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1814_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1814_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1814_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1814_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1814,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[3,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[0,4,2],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[557,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1815","image_path":"images/combination3d_1815.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1815_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1815_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1815_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1815_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_1815_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1815,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[0,3,4],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[4,0,0],[4,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[4,1,0]]],"total_cube_count":14}],"canvas_size":[587,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1816","image_path":"images/combination3d_1816.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1816_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1816_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1816_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1816_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1816_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1816,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,2],[1,2,1],[1,2,2],[1,2,3],[1,2,4],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[1,5,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[2,0,0],[2,0,1]],[[0,0,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":14}],"canvas_size":[619,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1817","image_path":"images/combination3d_1817.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1817_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1817_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1817_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1817_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1817_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1817,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,1,0],[4,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,1,0],[4,1,0],[4,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":10}],"canvas_size":[571,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1818","image_path":"images/combination3d_1818.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1818_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1818_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1818_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1818_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1818_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1818,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,2,1],[1,2,3]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[607,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1819","image_path":"images/combination3d_1819.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1819_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1819_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1819_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1819_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1819_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1819,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,4,0],[2,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,2],[0,1,3],[1,0,3],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[569,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1820","image_path":"images/combination3d_1820.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1820_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1820_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1820_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1820_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1820_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1820,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,1],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[595,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1821","image_path":"images/combination3d_1821.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1821_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1821_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1821_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1821_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1821_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1821,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[596,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1822","image_path":"images/combination3d_1822.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1822_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1822_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1822_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1822_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1822_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1822,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8}],"canvas_size":[585,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1823","image_path":"images/combination3d_1823.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1823_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1823_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1823_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_1823_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1823_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1823,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[579,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1824","image_path":"images/combination3d_1824.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1824_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1824_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1824_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1824_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1824_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1824,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[3,0,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,1,0],[0,1,1],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":10}],"canvas_size":[553,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1825","image_path":"images/combination3d_1825.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1825_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1825_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1825_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1825_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1825_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1825,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,3],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":13}],"canvas_size":[569,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1826","image_path":"images/combination3d_1826.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1826_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1826_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1826_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1826_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1826_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1826,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[3,1,0],[3,2,0],[4,0,0],[4,1,0],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[585,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1827","image_path":"images/combination3d_1827.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1827_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1827_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1827_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1827_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1827_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1827,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,5,0],[3,2,0],[3,2,1],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[556,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1828","image_path":"images/combination3d_1828.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1828_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1828_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1828_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1828_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1828_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1828,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":9}],"canvas_size":[595,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1829","image_path":"images/combination3d_1829.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1829_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1829_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1829_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1829_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1829_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1829,"target_cube_count":9,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,1],[1,1,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":12}],"canvas_size":[613,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1830","image_path":"images/combination3d_1830.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1830_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1830_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1830_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1830_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1830_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1830,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[2,0,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0],[4,1,1],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,0],[2,4,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,0,2],[2,0,3],[2,1,3]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[1,0,1],[1,2,1],[1,2,2],[1,3,1],[2,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[614,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1831","image_path":"images/combination3d_1831.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1831_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1831_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1831_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1831_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1831_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1831,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,0],[2,4,0],[2,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,0,2],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[613,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1832","image_path":"images/combination3d_1832.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1832_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1832_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1832_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1832_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1832_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1832,"target_cube_count":12,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,2,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1]],[[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,3]]],"total_cube_count":14}],"canvas_size":[583,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1833","image_path":"images/combination3d_1833.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1833_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1833_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1833_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1833_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1833_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1833,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,1],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":10}],"canvas_size":[599,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1834","image_path":"images/combination3d_1834.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1834_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1834_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1834_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1834_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1834_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1834,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11}],"canvas_size":[562,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1835","image_path":"images/combination3d_1835.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1835_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1835_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1835_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1835_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1835_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1835,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[576,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1836","image_path":"images/combination3d_1836.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1836_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1836_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1836_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1836_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1836_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1836,"target_cube_count":12,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[615,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1837","image_path":"images/combination3d_1837.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1837_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1837_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1837_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1837_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,5","question_id":"combination3d_1837_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1837,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[0,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[5,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,3],[1,0,4]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[571,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1838","image_path":"images/combination3d_1838.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1838_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1838_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1838_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1838_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1838_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1838,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,0,1],[4,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,1],[0,3,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,3,1]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":14}],"canvas_size":[556,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1839","image_path":"images/combination3d_1839.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1839_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1839_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1839_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1839_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1839_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1839,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[609,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1840","image_path":"images/combination3d_1840.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1840_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1840_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1840_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1840_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1840_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1840,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0],[3,0,1],[3,1,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,2],[2,2,0],[2,2,2],[2,2,3]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,1],[0,1,2],[0,3,1],[0,3,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,2],[3,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,2],[2,2,0],[2,2,2],[2,2,3],[2,3,3]]],"total_cube_count":15}],"canvas_size":[570,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1841","image_path":"images/combination3d_1841.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1841_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1841_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1841_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1841_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1841_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1841,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,2,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[571,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1842","image_path":"images/combination3d_1842.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1842_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1842_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1842_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1842_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1842_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1842,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[2,2,0],[2,3,0],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1],[2,0,2],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[600,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1843","image_path":"images/combination3d_1843.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1843_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1843_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1843_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_1843_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1843_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1843,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,3,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,2],[2,1,1],[2,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,2,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[2,0,2],[2,1,1],[3,0,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[616,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1844","image_path":"images/combination3d_1844.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1844_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1844_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1844_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1844_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1844_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1844,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[561,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1845","image_path":"images/combination3d_1845.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1845_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1845_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1845_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1845_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1845_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1845,"target_cube_count":12,"target_cubes":[[0,1,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[613,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1846","image_path":"images/combination3d_1846.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1846_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1846_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1846_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1846_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1846_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1846,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,3]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,2],[1,0,1],[1,1,1],[1,2,1],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[556,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1847","image_path":"images/combination3d_1847.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1847_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1847_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1847_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1847_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_1847_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1847,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[0,4,1],[0,5,1],[1,3,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[611,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1848","image_path":"images/combination3d_1848.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1848_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1848_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1848_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1848_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1848_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1848,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1]]],"total_cube_count":11}],"canvas_size":[587,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1849","image_path":"images/combination3d_1849.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1849_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1849_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1849_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1849_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1849_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1849,"target_cube_count":11,"target_cubes":[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0]]],"total_cube_count":9}],"canvas_size":[615,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1850","image_path":"images/combination3d_1850.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1850_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1850_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1850_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1850_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1850_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1850,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,4],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,1,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[600,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1851","image_path":"images/combination3d_1851.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1851_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1851_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1851_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1851_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_1851_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1851,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[0,1,4],[0,1,5],[1,0,1],[1,1,3],[2,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[1,5,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,2],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,5,0]]],"total_cube_count":13}],"canvas_size":[559,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1852","image_path":"images/combination3d_1852.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1852_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1852_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1852_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1852_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1852_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1852,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,5,0],[1,6,0],[1,7,0],[1,8,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,1],[0,0,2],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,2,0],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,1],[0,0,2],[0,1,1],[0,2,0],[0,2,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[580,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1853","image_path":"images/combination3d_1853.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1853_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1853_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1853_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1853_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1853_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1853,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,1,1],[3,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[592,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1854","image_path":"images/combination3d_1854.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1854_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1854_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1854_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1854_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1854_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1854,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,0,3],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13}],"canvas_size":[587,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1855","image_path":"images/combination3d_1855.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1855_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1855_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1855_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1855_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1855_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1855,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[613,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1856","image_path":"images/combination3d_1856.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1856_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1856_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1856_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1856_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1856_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1856,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":10}],"canvas_size":[574,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1857","image_path":"images/combination3d_1857.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1857_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1857_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1857_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1857_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1857_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1857,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11}],"canvas_size":[606,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1858","image_path":"images/combination3d_1858.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1858_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1858_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1858_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1858_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1858_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1858,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,1,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,2],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":13}],"canvas_size":[597,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1859","image_path":"images/combination3d_1859.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1859_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1859_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1859_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1859_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1859_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1859,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,0],[1,1,2],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[594,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1860","image_path":"images/combination3d_1860.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1860_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1860_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1860_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1860_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1860_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1860,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0]]],"total_cube_count":12}],"canvas_size":[612,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1861","image_path":"images/combination3d_1861.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1861_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1861_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1861_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1861_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1861_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1861,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[1,2,1],[2,0,0],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,2],[0,2,3],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[584,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1862","image_path":"images/combination3d_1862.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1862_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1862_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1862_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1862_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1862_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1862,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,1],[2,2,2],[2,3,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,3,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[599,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1863","image_path":"images/combination3d_1863.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1863_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1863_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1863_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1863_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1863_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1863,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":10}],"canvas_size":[558,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1864","image_path":"images/combination3d_1864.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1864_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1864_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1864_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1864_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1864_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1864,"target_cube_count":10,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[1,2,2],[2,1,1],[2,2,1],[2,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":14}],"canvas_size":[571,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1865","image_path":"images/combination3d_1865.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1865_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1865_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1865_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1865_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1865_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1865,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2]]],"total_cube_count":10}],"canvas_size":[610,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1866","image_path":"images/combination3d_1866.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1866_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1866_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1866_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1866_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1866_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1866,"target_cube_count":10,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,0,0],[1,0,2],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[2,1,0],[2,2,0],[2,2,2]]],"total_cube_count":14}],"canvas_size":[581,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1867","image_path":"images/combination3d_1867.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1867_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1867_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1867_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1867_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1867_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1867,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,1,1],[1,2,1],[1,3,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1],[3,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0]],[[0,0,1],[0,0,2],[1,0,1],[2,0,1],[3,0,0],[3,0,1],[3,0,2],[3,1,1],[3,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[1,0,3],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1]]],"total_cube_count":13}],"canvas_size":[609,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1868","image_path":"images/combination3d_1868.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1868_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1868_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1868_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_1868_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1868_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1868,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,2,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14}],"canvas_size":[578,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1869","image_path":"images/combination3d_1869.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1869_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1869_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1869_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_1869_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1869_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1869,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[2,3,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9}],"canvas_size":[592,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1870","image_path":"images/combination3d_1870.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1870_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1870_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1870_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1870_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1870_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1870,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,1],[2,2,1],[2,2,2]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,2,1],[1,2,2]],[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,1],[2,2,1]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,1],[1,0,2]]],"total_cube_count":14}],"canvas_size":[611,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1871","image_path":"images/combination3d_1871.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1871_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1871_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1871_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1871_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_1871_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1871,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[584,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1872","image_path":"images/combination3d_1872.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1872_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1872_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1872_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1872_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1872_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1872,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,3],[1,0,4]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":15}],"canvas_size":[551,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1873","image_path":"images/combination3d_1873.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1873_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1873_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1873_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_1873_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1873_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1873,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,1,0],[1,1,1],[2,0,1]]],"total_cube_count":10}],"canvas_size":[597,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1874","image_path":"images/combination3d_1874.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1874_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1874_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1874_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1874_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1874_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1874,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[580,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1875","image_path":"images/combination3d_1875.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1875_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1875_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1875_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1875_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1875_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1875,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8}],"canvas_size":[598,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1876","image_path":"images/combination3d_1876.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1876_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1876_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1876_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1876_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1876_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1876,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,1],[2,2,0]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[1,0,2],[1,0,3],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[2,0,5],[2,1,4],[3,0,3]]],"total_cube_count":14}],"canvas_size":[569,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1877","image_path":"images/combination3d_1877.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1877_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1877_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1877_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1877_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1877_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1877,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,3,0],[2,3,1],[2,3,2],[3,1,0],[3,2,0],[3,3,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[619,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1878","image_path":"images/combination3d_1878.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1878_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1878_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1878_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1878_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1878_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1878,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,2,1],[1,2,2],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[579,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1879","image_path":"images/combination3d_1879.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1879_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1879_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1879_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1879_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1879_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1879,"target_cube_count":13,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,1,1],[1,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[552,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1880","image_path":"images/combination3d_1880.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1880_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1880_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1880_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1880_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1880_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1880,"target_cube_count":13,"target_cubes":[[0,0,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[589,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1881","image_path":"images/combination3d_1881.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1881_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1881_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1881_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1881_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1881_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1881,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,0,0],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[606,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1882","image_path":"images/combination3d_1882.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1882_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1882_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1882_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1882_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1882_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1882,"target_cube_count":13,"target_cubes":[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,1],[2,0,2],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[2,1,1],[2,1,2],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[599,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1883","image_path":"images/combination3d_1883.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1883_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1883_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1883_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1883_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1883_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1883,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,3]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,2],[1,0,3],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":13}],"canvas_size":[565,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1884","image_path":"images/combination3d_1884.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1884_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1884_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1884_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1884_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1884_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1884,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[600,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1885","image_path":"images/combination3d_1885.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1885_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1885_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1885_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1885_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1885_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1885,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[554,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1886","image_path":"images/combination3d_1886.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1886_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1886_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1886_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1886_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1886_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1886,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11}],"canvas_size":[594,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1887","image_path":"images/combination3d_1887.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1887_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1887_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1887_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1887_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1887_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1887,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[612,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1888","image_path":"images/combination3d_1888.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1888_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1888_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1888_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_1888_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1888_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1888,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,2,3],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":15}],"canvas_size":[588,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1889","image_path":"images/combination3d_1889.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1889_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1889_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1889_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1889_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1889_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1889,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,1],[1,2,2],[1,3,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2],[3,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[598,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1890","image_path":"images/combination3d_1890.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1890_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1890_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1890_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1890_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1890_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1890,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,1,2],[0,2,2],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,3,0],[0,3,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0]]],"total_cube_count":13}],"canvas_size":[553,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1891","image_path":"images/combination3d_1891.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1891_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1891_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1891_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1891_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1891_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1891,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,2,2],[1,2,1],[1,2,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[3,0,0],[3,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":13}],"canvas_size":[589,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1892","image_path":"images/combination3d_1892.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1892_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1892_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1892_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_1892_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1892_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1892,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[601,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1893","image_path":"images/combination3d_1893.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1893_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1893_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1893_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1893_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1893_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1893,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,2,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1],[2,0,2],[3,0,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":11}],"canvas_size":[616,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1894","image_path":"images/combination3d_1894.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1894_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1894_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1894_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1894_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1894_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1894,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[588,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1895","image_path":"images/combination3d_1895.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1895_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1895_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1895_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1895_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1895_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1895,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,1,3],[0,2,3],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2],[1,3,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[563,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1896","image_path":"images/combination3d_1896.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1896_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1896_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1896_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1896_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1896_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1896,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[613,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1897","image_path":"images/combination3d_1897.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1897_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1897_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1897_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1897_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1897_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1897,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,3]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[589,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1898","image_path":"images/combination3d_1898.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1898_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1898_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1898_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1898_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1898_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1898,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,1,1],[1,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":9}],"canvas_size":[569,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1899","image_path":"images/combination3d_1899.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1899_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1899_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1899_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1899_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1899_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1899,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[555,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1900","image_path":"images/combination3d_1900.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1900_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1900_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1900_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1900_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1900_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1900,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":8}],"canvas_size":[617,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1901","image_path":"images/combination3d_1901.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1901_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1901_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1901_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1901_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1901_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1901,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[553,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1902","image_path":"images/combination3d_1902.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1902_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1902_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1902_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1902_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1902_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1902,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":10}],"canvas_size":[573,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1903","image_path":"images/combination3d_1903.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1903_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1903_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1903_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1903_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1903_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1903,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[611,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1904","image_path":"images/combination3d_1904.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1904_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1904_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1904_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1904_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1904_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1904,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[3,0,0],[3,1,0],[4,0,0],[4,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[3,0,0],[3,1,0],[4,0,0],[4,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":13}],"canvas_size":[563,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1905","image_path":"images/combination3d_1905.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1905_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1905_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1905_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_1905_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1905_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1905,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[3,0,0],[3,1,0],[3,1,1],[4,0,0],[4,1,0],[4,1,1],[5,0,0],[5,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0]]],"total_cube_count":9}],"canvas_size":[577,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1906","image_path":"images/combination3d_1906.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1906_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1906_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1906_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1906_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1906_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1906,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,1,2],[1,1,3],[1,2,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12}],"canvas_size":[580,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1907","image_path":"images/combination3d_1907.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1907_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1907_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1907_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1907_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1907_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1907,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,2],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,2],[0,3,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,2,3]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[577,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1908","image_path":"images/combination3d_1908.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1908_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1908_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1908_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1908_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1908_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1908,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13}],"canvas_size":[584,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1909","image_path":"images/combination3d_1909.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1909_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1909_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1909_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1909_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_1909_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1909,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2]]],"total_cube_count":11}],"canvas_size":[557,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1910","image_path":"images/combination3d_1910.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1910_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1910_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1910_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1910_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1910_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1910,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,0,3],[1,1,2],[1,1,3]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[594,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1911","image_path":"images/combination3d_1911.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1911_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1911_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1911_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1911_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_1911_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1911,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[556,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1912","image_path":"images/combination3d_1912.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1912_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1912_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1912_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1912_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1912_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1912,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[614,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1913","image_path":"images/combination3d_1913.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1913_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1913_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1913_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1913_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_1913_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1913,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":10}],"canvas_size":[550,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1914","image_path":"images/combination3d_1914.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1914_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1914_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1914_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1914_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1914_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1914,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,3],[0,0,4],[0,0,5],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,0,1],[3,0,1],[4,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[616,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1915","image_path":"images/combination3d_1915.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1915_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1915_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1915_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1915_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,6","question_id":"combination3d_1915_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1915,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[555,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1916","image_path":"images/combination3d_1916.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1916_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1916_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1916_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1916_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1916_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1916,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,2,0],[1,2,2],[1,3,0],[1,3,1],[1,3,2],[2,3,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[2,0,2],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[579,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1917","image_path":"images/combination3d_1917.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1917_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1917_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1917_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1917_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1917_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1917,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,1],[3,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,2,0],[2,3,0]]],"total_cube_count":10}],"canvas_size":[559,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1918","image_path":"images/combination3d_1918.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1918_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1918_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1918_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1918_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1918_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1918,"target_cube_count":9,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,2]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[593,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1919","image_path":"images/combination3d_1919.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1919_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1919_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1919_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1919_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_1919_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1919,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[613,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1920","image_path":"images/combination3d_1920.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1920_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1920_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1920_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1920_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1920_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1920,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,2,0],[4,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[551,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1921","image_path":"images/combination3d_1921.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1921_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1921_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1921_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1921_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1921_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1921,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[554,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1922","image_path":"images/combination3d_1922.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1922_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1922_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1922_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1922_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1922_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1922,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[612,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1923","image_path":"images/combination3d_1923.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1923_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1923_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1923_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1923_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1923_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1923,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10}],"canvas_size":[586,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1924","image_path":"images/combination3d_1924.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1924_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1924_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1924_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1924_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_1924_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1924,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":8}],"canvas_size":[568,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1925","image_path":"images/combination3d_1925.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1925_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1925_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1925_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1925_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1925_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1925,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1],[1,0,2]],[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,1],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12}],"canvas_size":[588,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1926","image_path":"images/combination3d_1926.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1926_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1926_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1926_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1926_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1926_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1926,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,1,0],[1,1,1],[1,1,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[589,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1927","image_path":"images/combination3d_1927.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1927_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1927_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1927_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1927_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1927_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1927,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[0,1,3],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,0,2],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[567,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1928","image_path":"images/combination3d_1928.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1928_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1928_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1928_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1928_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1928_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1928,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[553,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1929","image_path":"images/combination3d_1929.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1929_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1929_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1929_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1929_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_1929_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1929,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10}],"canvas_size":[580,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1930","image_path":"images/combination3d_1930.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1930_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1930_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1930_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_1930_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1930_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1930,"target_cube_count":9,"target_cubes":[[0,0,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,5,0],[1,6,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3],[1,0,4],[1,0,5]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[0,4,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[610,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1931","image_path":"images/combination3d_1931.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1931_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1931_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1931_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,5","question_id":"combination3d_1931_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1931_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1931,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[592,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1932","image_path":"images/combination3d_1932.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1932_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1932_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1932_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1932_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_1932_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1932,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,0,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2]]],"total_cube_count":10}],"canvas_size":[591,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1933","image_path":"images/combination3d_1933.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1933_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1933_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1933_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1933_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1933_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1933,"target_cube_count":10,"target_cubes":[[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":14}],"canvas_size":[584,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1934","image_path":"images/combination3d_1934.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1934_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1934_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1934_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1934_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1934_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1934,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,1],[1,3,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,3]],[[0,1,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,3,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[1,2,1],[2,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":12}],"canvas_size":[569,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1935","image_path":"images/combination3d_1935.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1935_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1935_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1935_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1935_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1935_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1935,"target_cube_count":12,"target_cubes":[[0,3,0],[1,3,0],[2,3,0],[2,4,0],[2,4,1],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[3,2,1],[3,3,0],[4,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,1,1],[3,0,1],[3,1,0],[3,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12}],"canvas_size":[597,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1936","image_path":"images/combination3d_1936.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1936_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1936_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1936_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1936_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1936_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1936,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0],[3,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,3,0],[1,4,0],[2,3,0],[2,4,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,1],[0,3,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[568,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1937","image_path":"images/combination3d_1937.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1937_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1937_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1937_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1937_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1937_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1937,"target_cube_count":11,"target_cubes":[[0,2,0],[1,2,0],[1,3,0],[2,2,0],[2,2,1],[2,3,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]],[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[3,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[3,0,0],[3,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[616,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1938","image_path":"images/combination3d_1938.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1938_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1938_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1938_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1938_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1938_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1938,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[3,2,0],[3,3,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,3,1],[0,3,2],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":10}],"canvas_size":[580,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1939","image_path":"images/combination3d_1939.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1939_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1939_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1939_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1939_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_1939_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1939,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[587,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1940","image_path":"images/combination3d_1940.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1940_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1940_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1940_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1940_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1940_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1940,"target_cube_count":8,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[612,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1941","image_path":"images/combination3d_1941.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1941_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1941_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1941_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1941_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1941_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1941,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,1,1],[3,0,1],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[586,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1942","image_path":"images/combination3d_1942.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1942_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1942_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1942_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1942_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_1942_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1942,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":12}],"canvas_size":[557,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1943","image_path":"images/combination3d_1943.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1943_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1943_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1943_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1943_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1943_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1943,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[4,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[557,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1944","image_path":"images/combination3d_1944.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1944_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1944_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1944_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_1944_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1944_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1944,"target_cube_count":10,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[602,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1945","image_path":"images/combination3d_1945.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1945_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1945_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1945_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1945_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1945_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1945,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,2,0],[0,2,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2],[3,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,1]]],"total_cube_count":9}],"canvas_size":[576,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1946","image_path":"images/combination3d_1946.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1946_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1946_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1946_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1946_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1946_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1946,"target_cube_count":9,"target_cubes":[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[558,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1947","image_path":"images/combination3d_1947.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1947_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1947_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1947_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1947_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1947_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1947,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[603,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1948","image_path":"images/combination3d_1948.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1948_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1948_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1948_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_1948_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1948_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1948,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[620,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1949","image_path":"images/combination3d_1949.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1949_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1949_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1949_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1949_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1949_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1949,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[0,2,1],[1,0,1],[1,0,2],[1,0,3],[1,1,2],[1,1,3],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2],[4,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":14}],"canvas_size":[581,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1950","image_path":"images/combination3d_1950.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1950_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1950_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1950_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1950_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1950_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1950,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[0,1,4],[1,1,2]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14}],"canvas_size":[567,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1951","image_path":"images/combination3d_1951.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1951_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1951_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1951_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1951_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1951_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1951,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[594,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1952","image_path":"images/combination3d_1952.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1952_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1952_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1952_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1952_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1952_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1952,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]],[[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[2,0,0],[2,0,1],[2,1,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]],[[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1]]],"total_cube_count":14}],"canvas_size":[584,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1953","image_path":"images/combination3d_1953.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1953_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1953_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1953_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1953_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_1953_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1953,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[608,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1954","image_path":"images/combination3d_1954.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1954_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1954_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1954_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1954_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1954_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1954,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[3,0,2],[3,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[570,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1955","image_path":"images/combination3d_1955.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1955_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1955_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1955_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1955_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1955_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1955,"target_cube_count":12,"target_cubes":[[0,3,0],[0,4,0],[0,4,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3,1],[1,3,1],[2,0,1],[2,1,0],[2,1,1],[2,2,1],[2,3,1],[3,2,1],[3,3,1],[3,3,2]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[594,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1956","image_path":"images/combination3d_1956.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1956_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1956_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1956_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1956_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1956_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1956,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,3]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[613,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1957","image_path":"images/combination3d_1957.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1957_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1957_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1957_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_1957_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1957_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1957,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11}],"canvas_size":[581,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1958","image_path":"images/combination3d_1958.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1958_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1958_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1958_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1958_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1958_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1958,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[0,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[550,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1959","image_path":"images/combination3d_1959.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1959_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1959_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1959_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1959_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1959_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1959,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,3,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11}],"canvas_size":[584,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1960","image_path":"images/combination3d_1960.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1960_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1960_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1960_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_1960_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1960_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1960,"target_cube_count":11,"target_cubes":[[0,1,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,3,0],[2,3,1],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[0,2,2],[1,0,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,1,1],[2,0,0],[2,0,1],[2,1,1],[3,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[1,2,2],[2,0,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,0],[2,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[557,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1961","image_path":"images/combination3d_1961.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1961_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1961_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1961_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_1961_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1961_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1961,"target_cube_count":13,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":11}],"canvas_size":[573,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1962","image_path":"images/combination3d_1962.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1962_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1962_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1962_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1962_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1962_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1962,"target_cube_count":10,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1],[3,1,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[617,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1963","image_path":"images/combination3d_1963.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1963_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1963_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1963_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1963_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_1963_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1963,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[575,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1964","image_path":"images/combination3d_1964.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1964_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1964_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1964_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1964_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_1964_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1964,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,2],[1,1,1],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,1,1],[2,2,1],[2,2,2]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[592,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1965","image_path":"images/combination3d_1965.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1965_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1965_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1965_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1965_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1965_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1965,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":12}],"canvas_size":[554,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1966","image_path":"images/combination3d_1966.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1966_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1966_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1966_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_1966_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1966_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1966,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10}],"canvas_size":[591,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1967","image_path":"images/combination3d_1967.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1967_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1967_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1967_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_1967_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1967_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1967,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,1,1],[3,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2],[0,1,3]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,2,1],[2,3,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12}],"canvas_size":[568,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1968","image_path":"images/combination3d_1968.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1968_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1968_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1968_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_1968_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1968_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1968,"target_cube_count":12,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,2,1],[2,3,0],[3,2,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[601,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1969","image_path":"images/combination3d_1969.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1969_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1969_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1969_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1969_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1969_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1969,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,1],[2,0,1],[2,0,2],[2,0,3],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[567,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1970","image_path":"images/combination3d_1970.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1970_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1970_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1970_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1970_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1970_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1970,"target_cube_count":9,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,1,0],[3,0,0],[3,0,1],[3,0,2],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[575,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1971","image_path":"images/combination3d_1971.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1971_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1971_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1971_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1971_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_1971_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1971,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,1,3],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,1],[2,1,1],[3,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[577,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1972","image_path":"images/combination3d_1972.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1972_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1972_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1972_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_1972_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1972_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1972,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[572,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1973","image_path":"images/combination3d_1973.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1973_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1973_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1973_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1973_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1973_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1973,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,1,1],[2,2,1],[2,3,1],[2,3,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,1],[2,0,2],[2,1,1],[2,1,2],[3,0,1],[3,0,2],[3,1,1],[4,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[3,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[550,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1974","image_path":"images/combination3d_1974.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1974_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1974_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1974_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_1974_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1974_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1974,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0],[3,3,0],[3,3,1],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[0,4,2],[1,3,0],[1,4,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,2,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11}],"canvas_size":[573,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1975","image_path":"images/combination3d_1975.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1975_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1975_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1975_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1975_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_1975_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1975,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[550,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_1976","image_path":"images/combination3d_1976.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1976_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1976_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1976_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_1976_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1976_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1976,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12}],"canvas_size":[608,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1977","image_path":"images/combination3d_1977.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1977_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1977_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1977_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1977_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1977_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1977,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[2,0,0],[2,0,1],[2,1,1],[2,2,1],[3,2,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,2],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":10}],"canvas_size":[558,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1978","image_path":"images/combination3d_1978.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1978_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1978_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1978_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1978_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1978_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1978,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0],[3,3,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,3,0],[1,4,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9}],"canvas_size":[561,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1979","image_path":"images/combination3d_1979.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1979_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1979_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1979_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1979_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,6","question_id":"combination3d_1979_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1979,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,3],[2,1,3],[2,2,3]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[551,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_1980","image_path":"images/combination3d_1980.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1980_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1980_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1980_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1980_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1980_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1980,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,1],[2,0,3],[3,0,3]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[572,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_1981","image_path":"images/combination3d_1981.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1981_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1981_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1981_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1981_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1981_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1981,"target_cube_count":12,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,4],[1,0,4],[1,0,5],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14}],"canvas_size":[560,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_1982","image_path":"images/combination3d_1982.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1982_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1982_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1982_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1982_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_1982_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1982,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,3,0],[2,3,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[2,2,1],[3,0,0],[3,0,1],[3,0,2],[3,1,1],[3,2,1],[4,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[4,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[0,4,0],[1,1,1],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[564,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1983","image_path":"images/combination3d_1983.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1983_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1983_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1983_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1983_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_1983_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1983,"target_cube_count":13,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[4,0,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,1,1],[0,2,1],[1,1,1],[1,1,2],[1,2,1],[2,0,2],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[596,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_1984","image_path":"images/combination3d_1984.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1984_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1984_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1984_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1984_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_1984_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1984,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1],[1,2,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[601,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1985","image_path":"images/combination3d_1985.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1985_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1985_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1985_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1985_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_1985_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1985,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[2,3,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[583,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1986","image_path":"images/combination3d_1986.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1986_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1986_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1986_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_1986_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1986_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1986,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[1,0,1],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":12}],"canvas_size":[610,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1987","image_path":"images/combination3d_1987.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1987_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1987_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1987_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_1987_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1987_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1987,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[620,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_1988","image_path":"images/combination3d_1988.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_1988_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1988_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1988_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1988_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_1988_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1988,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,3]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,1],[2,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[571,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1989","image_path":"images/combination3d_1989.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1989_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1989_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1989_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_1989_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1989_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1989,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8}],"canvas_size":[551,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_1990","image_path":"images/combination3d_1990.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_1990_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1990_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_1990_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_1990_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_1990_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1990,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,1,1],[3,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2],[4,1,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[1,4,1],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":15}],"canvas_size":[604,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_1991","image_path":"images/combination3d_1991.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_1991_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1991_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1991_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_1991_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1991_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1991,"target_cube_count":14,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[1,4,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,1],[2,0,1],[2,1,0],[2,1,1],[3,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[592,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1992","image_path":"images/combination3d_1992.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1992_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1992_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1992_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1992_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_1992_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1992,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,1,0],[0,1,1],[1,1,1],[1,1,2],[2,0,1],[2,1,1]]],"total_cube_count":10}],"canvas_size":[611,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_1993","image_path":"images/combination3d_1993.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1993_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1993_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1993_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1993_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1993_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1993,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[3,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,2,0],[1,3,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,1,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,2]]],"total_cube_count":13}],"canvas_size":[611,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_1994","image_path":"images/combination3d_1994.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_1994_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1994_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1994_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_1994_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_1994_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1994,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,0,0],[2,0,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[608,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1995","image_path":"images/combination3d_1995.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1995_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1995_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1995_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1995_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1995_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1995,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[608,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_1996","image_path":"images/combination3d_1996.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_1996_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_1996_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_1996_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1996_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_1996_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1996,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,3,0],[2,3,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,1],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9}],"canvas_size":[580,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_1997","image_path":"images/combination3d_1997.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1997_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_1997_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_1997_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_1997_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_1997_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1997,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[575,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_1998","image_path":"images/combination3d_1998.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_1998_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_1998_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1998_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_1998_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_1998_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1998,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9}],"canvas_size":[564,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_1999","image_path":"images/combination3d_1999.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_1999_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_1999_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_1999_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_1999_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_1999_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":1999,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,2,0],[1,2,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[3,1,0],[3,2,0],[4,2,0],[5,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,0,3],[1,1,2],[1,1,3],[1,1,4],[2,1,4],[3,1,4]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,1],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0],[4,0,1],[4,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,1],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0],[4,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[607,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2000","image_path":"images/combination3d_2000.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2000_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2000_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2000_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2000_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2000_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2000,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,1,1],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14}],"canvas_size":[552,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2001","image_path":"images/combination3d_2001.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2001_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2001_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2001_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2001_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2001_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2001,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":10}],"canvas_size":[550,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2002","image_path":"images/combination3d_2002.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2002_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2002_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2002_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2002_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2002_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2002,"target_cube_count":10,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,3,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[3,1,1],[3,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1],[2,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[564,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2003","image_path":"images/combination3d_2003.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2003_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2003_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2003_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2003_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2003_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2003,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[617,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2004","image_path":"images/combination3d_2004.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2004_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2004_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2004_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2004_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2004_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2004,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,2,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[607,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2005","image_path":"images/combination3d_2005.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2005_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2005_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2005_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2005_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2005_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2005,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[1,2,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14}],"canvas_size":[600,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2006","image_path":"images/combination3d_2006.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2006_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2006_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2006_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2006_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2006_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2006,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[575,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2007","image_path":"images/combination3d_2007.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2007_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2007_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2007_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2007_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2007_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2007,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,2,0],[4,1,0],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,3],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[568,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2008","image_path":"images/combination3d_2008.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2008_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2008_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2008_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2008_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2008_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2008,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,1,0],[2,1,1],[2,2,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,1,0],[1,3,1],[2,3,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,0,2],[0,1,2],[0,1,3],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,2]]],"total_cube_count":14}],"canvas_size":[584,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2009","image_path":"images/combination3d_2009.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2009_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2009_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2009_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2009_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2009_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2009,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,0,1]]],"total_cube_count":11}],"canvas_size":[567,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2010","image_path":"images/combination3d_2010.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2010_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2010_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2010_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2010_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2010_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2010,"target_cube_count":11,"target_cubes":[[0,0,0],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,2],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[616,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2011","image_path":"images/combination3d_2011.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2011_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2011_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2011_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_2011_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2011_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2011,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[562,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2012","image_path":"images/combination3d_2012.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2012_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2012_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2012_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2012_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2012_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2012,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[604,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2013","image_path":"images/combination3d_2013.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2013_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2013_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2013_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2013_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2013_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2013,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[590,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2014","image_path":"images/combination3d_2014.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2014_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2014_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2014_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2014_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2014_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2014,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,3],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[559,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2015","image_path":"images/combination3d_2015.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2015_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2015_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2015_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2015_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2015_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2015,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":12}],"canvas_size":[607,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2016","image_path":"images/combination3d_2016.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2016_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2016_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2016_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2016_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2016_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2016,"target_cube_count":12,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]]],"total_cube_count":10}],"canvas_size":[575,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2017","image_path":"images/combination3d_2017.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2017_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2017_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2017_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2017_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2017_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2017,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[618,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2018","image_path":"images/combination3d_2018.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2018_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2018_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2018_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2018_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2018_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2018,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[3,0,0],[4,0,0],[5,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,2],[1,1,3]]],"total_cube_count":9}],"canvas_size":[569,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2019","image_path":"images/combination3d_2019.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2019_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2019_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2019_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2019_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2019_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2019,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":14}],"canvas_size":[572,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2020","image_path":"images/combination3d_2020.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2020_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2020_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2020_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2020_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2020_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2020,"target_cube_count":14,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[1,3,3],[1,4,0],[1,4,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[1,2,1],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,2]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":13}],"canvas_size":[601,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2021","image_path":"images/combination3d_2021.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2021_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2021_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2021_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2021_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2021_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2021,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[618,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2022","image_path":"images/combination3d_2022.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2022_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2022_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2022_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2022_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2022_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2022,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,2,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[2,1,1]]],"total_cube_count":11}],"canvas_size":[599,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2023","image_path":"images/combination3d_2023.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2023_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2023_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2023_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2023_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2023_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2023,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[610,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2024","image_path":"images/combination3d_2024.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2024_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2024_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2024_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2024_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2024_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2024,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[2,4,0],[2,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[4,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,3],[2,1,3],[3,1,3]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,3],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":14}],"canvas_size":[560,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2025","image_path":"images/combination3d_2025.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2025_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2025_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2025_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2025_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2025_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2025,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1],[3,0,2],[3,0,3],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,1],[1,1,1],[2,0,1],[2,1,1],[3,1,0],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,1],[1,1,1],[2,1,0],[2,1,1],[3,0,1],[3,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12}],"canvas_size":[565,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2026","image_path":"images/combination3d_2026.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2026_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2026_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2026_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2026_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2026_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2026,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,2,0],[1,3,0],[1,4,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[563,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2027","image_path":"images/combination3d_2027.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2027_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2027_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2027_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2027_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_2027_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2027,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":9}],"canvas_size":[595,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2028","image_path":"images/combination3d_2028.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2028_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2028_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2028_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2028_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2028_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2028,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[4,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[4,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[613,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2029","image_path":"images/combination3d_2029.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2029_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2029_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2029_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2029_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2029_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2029,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,1,1],[2,1,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[586,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2030","image_path":"images/combination3d_2030.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2030_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2030_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2030_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2030_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2030_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2030,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,2,1],[2,3,1],[3,2,1],[3,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[572,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2031","image_path":"images/combination3d_2031.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2031_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2031_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2031_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2031_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2031_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2031,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[3,2,0],[3,3,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,2,3],[2,0,1],[2,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[1,0,2],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0]]],"total_cube_count":13}],"canvas_size":[554,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2032","image_path":"images/combination3d_2032.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2032_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2032_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2032_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2032_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2032_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2032,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[3,3,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[602,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2033","image_path":"images/combination3d_2033.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2033_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2033_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2033_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2033_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2033_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2033,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[559,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2034","image_path":"images/combination3d_2034.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2034_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2034_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2034_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2034_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2034_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2034,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9}],"canvas_size":[588,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2035","image_path":"images/combination3d_2035.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2035_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2035_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2035_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2035_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2035_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2035,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[557,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2036","image_path":"images/combination3d_2036.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2036_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2036_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2036_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2036_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2036_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2036,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,1],[2,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[582,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2037","image_path":"images/combination3d_2037.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2037_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2037_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2037_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2037_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2037_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2037,"target_cube_count":12,"target_cubes":[[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[2,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,1]]],"total_cube_count":11}],"canvas_size":[561,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2038","image_path":"images/combination3d_2038.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2038_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2038_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2038_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2038_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2038_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2038,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,3]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,1,0],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":11}],"canvas_size":[618,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2039","image_path":"images/combination3d_2039.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2039_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2039_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2039_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2039_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2039_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2039,"target_cube_count":11,"target_cubes":[[0,3,0],[0,4,0],[0,4,1],[0,5,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,4,0],[2,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12}],"canvas_size":[598,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2040","image_path":"images/combination3d_2040.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2040_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2040_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2040_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_2040_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2040_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2040,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]]],"total_cube_count":14}],"canvas_size":[555,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2041","image_path":"images/combination3d_2041.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2041_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2041_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2041_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2041_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2041_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2041,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[0,1,4]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,4,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[0,1,4]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[592,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2042","image_path":"images/combination3d_2042.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2042_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2042_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2042_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_2042_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2042_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2042,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[611,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2043","image_path":"images/combination3d_2043.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2043_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2043_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2043_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_2043_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2043_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2043,"target_cube_count":9,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[565,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2044","image_path":"images/combination3d_2044.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2044_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2044_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2044_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2044_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_2044_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2044,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[566,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2045","image_path":"images/combination3d_2045.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2045_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2045_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2045_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2045_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2045_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2045,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[601,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2046","image_path":"images/combination3d_2046.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2046_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2046_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2046_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2046_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2046_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2046,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[578,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2047","image_path":"images/combination3d_2047.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2047_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2047_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2047_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2047_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2047_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2047,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[4,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2],[1,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[586,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2048","image_path":"images/combination3d_2048.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2048_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2048_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2048_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2048_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2048_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2048,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[3,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[3,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":8}],"canvas_size":[616,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2049","image_path":"images/combination3d_2049.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2049_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2049_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2049_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_2049_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2049_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2049,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[592,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2050","image_path":"images/combination3d_2050.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2050_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2050_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2050_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2050_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2050_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2050,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,1,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":12}],"canvas_size":[576,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2051","image_path":"images/combination3d_2051.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2051_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2051_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2051_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2051_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2051_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2051,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[592,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2052","image_path":"images/combination3d_2052.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2052_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2052_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2052_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2052_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2052_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2052,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2],[0,3,1],[1,0,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[587,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2053","image_path":"images/combination3d_2053.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2053_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2053_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2053_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2053_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_2053_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2053,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[577,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2054","image_path":"images/combination3d_2054.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2054_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2054_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2054_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2054_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2054_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2054,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[571,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2055","image_path":"images/combination3d_2055.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2055_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2055_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2055_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2055_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2055_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2055,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[614,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2056","image_path":"images/combination3d_2056.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2056_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2056_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2056_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2056_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2056_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2056,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[1,2,0],[1,3,0],[2,3,0],[3,3,0],[3,3,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,3],[0,2,2],[0,2,3],[0,3,0],[0,3,1],[0,3,2],[1,0,3],[1,3,0],[2,0,3],[3,0,3]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,3],[0,2,0],[1,2,0],[1,3,0],[2,3,0],[3,3,0],[3,3,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":15}],"canvas_size":[608,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2057","image_path":"images/combination3d_2057.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2057_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2057_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2057_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2057_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2057_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2057,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,4,1],[2,3,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[569,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2058","image_path":"images/combination3d_2058.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2058_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2058_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2058_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2058_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2058_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2058,"target_cube_count":8,"target_cubes":[[0,0,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,1],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[603,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2059","image_path":"images/combination3d_2059.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2059_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2059_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2059_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2059_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2059_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2059,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[587,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2060","image_path":"images/combination3d_2060.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2060_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2060_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2060_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2060_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2060_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2060,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":10}],"canvas_size":[596,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2061","image_path":"images/combination3d_2061.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2061_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2061_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2061_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2061_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2061_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2061,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]]],"total_cube_count":11}],"canvas_size":[592,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2062","image_path":"images/combination3d_2062.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2062_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2062_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2062_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2062_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2062_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2062,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[1,3,1]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[1,0,0],[1,0,2]],[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,3,0]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[569,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2063","image_path":"images/combination3d_2063.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2063_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2063_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2063_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2063_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2063_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2063,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[2,2,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[3,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":13}],"canvas_size":[588,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2064","image_path":"images/combination3d_2064.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2064_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2064_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2064_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_2064_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2064_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2064,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[0,2,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":9}],"canvas_size":[582,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2065","image_path":"images/combination3d_2065.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2065_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2065_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2065_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_2065_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2065_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2065,"target_cube_count":9,"target_cubes":[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[3,3,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[565,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2066","image_path":"images/combination3d_2066.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2066_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2066_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2066_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2066_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2066_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2066,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,2],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":9}],"canvas_size":[561,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2067","image_path":"images/combination3d_2067.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2067_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2067_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2067_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2067_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2067_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2067,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[1,1,3],[1,2,2],[2,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[559,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2068","image_path":"images/combination3d_2068.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2068_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2068_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2068_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_2068_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2068_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2068,"target_cube_count":11,"target_cubes":[[0,2,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[1,3,0]],[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,1],[2,2,0],[2,2,1],[3,2,1]]],"total_cube_count":14}],"canvas_size":[596,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2069","image_path":"images/combination3d_2069.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2069_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2069_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2069_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2069_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2069_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2069,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,1,0],[3,1,1],[3,1,2],[3,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[599,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2070","image_path":"images/combination3d_2070.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2070_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2070_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2070_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2070_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2070_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2070,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,1,0],[2,1,1],[3,0,1],[3,1,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[550,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2071","image_path":"images/combination3d_2071.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2071_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2071_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2071_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_2071_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2071_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2071,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,2],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[2,0,0],[2,0,1],[3,0,1],[3,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[0,4,2],[0,4,3]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,0,4],[2,0,0],[2,0,1],[2,0,4],[3,0,4]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[0,4,2],[0,4,3]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[594,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2072","image_path":"images/combination3d_2072.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2072_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2072_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2072_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2072_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2072_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2072,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[1,4,2],[1,4,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,3,1],[2,1,1]]],"total_cube_count":14}],"canvas_size":[575,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2073","image_path":"images/combination3d_2073.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2073_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2073_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2073_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2073_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2073_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2073,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[2,3,1],[2,3,2],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,2],[1,0,2],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":15}],"canvas_size":[584,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2074","image_path":"images/combination3d_2074.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2074_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2074_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2074_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2074_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2074_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2074,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,0],[1,1,2]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[591,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2075","image_path":"images/combination3d_2075.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2075_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2075_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2075_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2075_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2075_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2075,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0]]],"total_cube_count":8}],"canvas_size":[575,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2076","image_path":"images/combination3d_2076.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2076_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2076_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2076_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2076_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2076_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2076,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9}],"canvas_size":[594,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2077","image_path":"images/combination3d_2077.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2077_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2077_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2077_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2077_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2077_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2077,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[555,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2078","image_path":"images/combination3d_2078.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2078_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2078_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2078_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2078_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2078_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2078,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[608,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2079","image_path":"images/combination3d_2079.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2079_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2079_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2079_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2079_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2079_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2079,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1],[3,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,1],[2,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0]]],"total_cube_count":11}],"canvas_size":[555,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2080","image_path":"images/combination3d_2080.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2080_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2080_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2080_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2080_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2080_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2080,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1],[2,5,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,2,1],[2,1,0],[2,1,1],[2,2,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[610,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2081","image_path":"images/combination3d_2081.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2081_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2081_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2081_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2081_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2081_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2081,"target_cube_count":14,"target_cubes":[[0,3,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[2,4,0],[2,4,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[564,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2082","image_path":"images/combination3d_2082.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2082_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2082_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2082_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_2082_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2082_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2082,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[552,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2083","image_path":"images/combination3d_2083.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2083_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2083_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2083_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2083_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2083_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2083,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,2],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,2,1],[2,2,1],[3,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]]],"total_cube_count":12}],"canvas_size":[605,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2084","image_path":"images/combination3d_2084.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2084_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2084_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2084_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2084_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2084_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2084,"target_cube_count":12,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,2]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,2],[0,1,3],[1,1,1],[1,1,2],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,3,0]]],"total_cube_count":13}],"canvas_size":[561,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2085","image_path":"images/combination3d_2085.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2085_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2085_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2085_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2085_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2085_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2085,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,0,2],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,3],[2,0,4]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":12}],"canvas_size":[584,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2086","image_path":"images/combination3d_2086.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2086_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2086_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2086_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2086_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2086_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2086,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[566,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2087","image_path":"images/combination3d_2087.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2087_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2087_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2087_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2087_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2087_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2087,"target_cube_count":9,"target_cubes":[[0,2,0],[0,3,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,1,1],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,2,0],[1,2,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,2,0]]],"total_cube_count":14}],"canvas_size":[612,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2088","image_path":"images/combination3d_2088.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2088_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2088_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2088_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2088_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2088_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2088,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,2]]],"total_cube_count":8}],"canvas_size":[598,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2089","image_path":"images/combination3d_2089.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2089_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2089_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2089_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2089_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2089_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2089,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[2,0,2]]],"total_cube_count":10}],"canvas_size":[581,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2090","image_path":"images/combination3d_2090.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2090_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2090_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2090_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2090_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2090_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2090,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8}],"canvas_size":[587,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2091","image_path":"images/combination3d_2091.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2091_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2091_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2091_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2091_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2091_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2091,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[604,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2092","image_path":"images/combination3d_2092.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2092_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2092_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2092_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2092_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2092_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2092,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,0,2],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,1,3],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12}],"canvas_size":[604,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2093","image_path":"images/combination3d_2093.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2093_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2093_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2093_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2093_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2093_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2093,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[1,2,1],[2,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":8}],"canvas_size":[556,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2094","image_path":"images/combination3d_2094.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2094_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2094_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2094_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2094_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2094_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2094,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0]]],"total_cube_count":9}],"canvas_size":[585,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2095","image_path":"images/combination3d_2095.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2095_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2095_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2095_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2095_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2095_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2095,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[552,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2096","image_path":"images/combination3d_2096.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2096_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2096_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2096_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2096_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2096_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2096,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[1,3,3],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,1,1]],[[0,0,2],[0,0,3],[0,1,2],[0,2,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,1],[2,3,2],[2,3,3],[3,3,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[1,2,2],[1,3,0],[1,3,1],[1,3,2],[1,3,3],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15}],"canvas_size":[560,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2097","image_path":"images/combination3d_2097.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2097_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2097_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2097_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2097_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2097_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2097,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[1,3,3],[2,1,0],[2,1,1],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1]]],"total_cube_count":13}],"canvas_size":[580,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2098","image_path":"images/combination3d_2098.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2098_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2098_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2098_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2098_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2098_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2098,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,1,2],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[604,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2099","image_path":"images/combination3d_2099.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2099_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2099_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2099_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2099_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2099_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2099,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]]],"total_cube_count":8}],"canvas_size":[587,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2100","image_path":"images/combination3d_2100.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2100_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2100_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2100_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2100_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2100_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2100,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[0,1,1],[1,0,2],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":14}],"canvas_size":[596,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2101","image_path":"images/combination3d_2101.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2101_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2101_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2101_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2101_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2101_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2101,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,2,0],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[588,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2102","image_path":"images/combination3d_2102.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2102_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2102_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2102_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2102_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_2102_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2102,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[560,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2103","image_path":"images/combination3d_2103.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2103_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2103_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2103_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_2103_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2103_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2103,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[573,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2104","image_path":"images/combination3d_2104.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2104_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2104_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2104_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2104_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2104_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2104,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[4,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[568,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2105","image_path":"images/combination3d_2105.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2105_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2105_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2105_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2105_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2105_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2105,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[598,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2106","image_path":"images/combination3d_2106.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2106_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2106_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2106_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2106_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2106_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2106,"target_cube_count":12,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[1,1,3],[2,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[554,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2107","image_path":"images/combination3d_2107.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2107_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2107_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2107_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2107_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2107_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2107,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10}],"canvas_size":[582,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2108","image_path":"images/combination3d_2108.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2108_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2108_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2108_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2108_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2108_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2108,"target_cube_count":10,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11}],"canvas_size":[600,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2109","image_path":"images/combination3d_2109.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2109_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2109_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2109_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2109_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2109_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2109,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[564,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2110","image_path":"images/combination3d_2110.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2110_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2110_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2110_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2110_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2110_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2110,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,3]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]]],"total_cube_count":10}],"canvas_size":[594,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2111","image_path":"images/combination3d_2111.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2111_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2111_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2111_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2111_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2111_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2111,"target_cube_count":10,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,2],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[2,1,1],[2,1,2],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,2,2],[1,2,3],[2,1,1],[2,1,2],[2,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,1],[1,2,2],[2,1,0],[2,1,1],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[562,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2112","image_path":"images/combination3d_2112.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2112_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2112_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2112_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2112_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2112_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2112,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,1,2]]],"total_cube_count":10}],"canvas_size":[551,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2113","image_path":"images/combination3d_2113.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2113_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2113_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2113_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2113_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2113_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2113,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,3],[0,1,3],[0,2,1],[0,2,2],[0,2,3],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,2,0],[3,2,1],[3,2,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,1],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[2,1,2],[2,2,1],[3,2,0],[3,2,1],[3,2,2],[3,2,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,3],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1],[1,2,2],[1,3,1],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[580,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2114","image_path":"images/combination3d_2114.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2114_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2114_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2114_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2114_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2114_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2114,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":10}],"canvas_size":[595,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2115","image_path":"images/combination3d_2115.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2115_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2115_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2115_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2115_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2115_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2115,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[569,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2116","image_path":"images/combination3d_2116.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2116_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2116_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2116_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2116_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2116_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2116,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":11}],"canvas_size":[574,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2117","image_path":"images/combination3d_2117.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2117_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2117_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2117_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2117_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2117_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2117,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[605,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2118","image_path":"images/combination3d_2118.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2118_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2118_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2118_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2118_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2118_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2118,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[3,1,0],[3,2,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,2,1],[1,0,3]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[572,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2119","image_path":"images/combination3d_2119.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2119_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2119_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2119_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2119_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2119_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2119,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[606,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2120","image_path":"images/combination3d_2120.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2120_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2120_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2120_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2120_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2120_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2120,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14}],"canvas_size":[572,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2121","image_path":"images/combination3d_2121.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2121_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2121_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2121_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2121_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2121_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2121,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[600,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2122","image_path":"images/combination3d_2122.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2122_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2122_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2122_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2122_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2122_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2122,"target_cube_count":11,"target_cubes":[[0,3,0],[1,1,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[3,2,0],[3,3,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,2,0]],[[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[2,2,1],[3,1,1]]],"total_cube_count":14}],"canvas_size":[602,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2123","image_path":"images/combination3d_2123.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2123_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2123_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2123_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2123_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2123_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2123,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,3]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,0,3],[2,1,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0],[3,0,1],[3,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[551,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2124","image_path":"images/combination3d_2124.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2124_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2124_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2124_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2124_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2124_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2124,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,1,1],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,1,1],[1,1,2]]],"total_cube_count":14}],"canvas_size":[590,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2125","image_path":"images/combination3d_2125.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2125_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2125_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2125_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2125_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2125_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2125,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,3,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,1,2],[2,1,3],[3,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,3,0],[2,3,1],[2,4,0],[3,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[581,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2126","image_path":"images/combination3d_2126.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2126_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2126_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2126_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2126_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2126_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2126,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[2,0,1],[2,1,1],[2,2,1],[2,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[565,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2127","image_path":"images/combination3d_2127.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2127_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2127_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2127_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2127_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2127_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2127,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[564,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2128","image_path":"images/combination3d_2128.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2128_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2128_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2128_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2128_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2128_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2128,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[569,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2129","image_path":"images/combination3d_2129.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2129_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2129_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2129_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2129_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2129_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2129,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10}],"canvas_size":[578,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2130","image_path":"images/combination3d_2130.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2130_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2130_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2130_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2130_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,6","question_id":"combination3d_2130_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2130,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":11}],"canvas_size":[600,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2131","image_path":"images/combination3d_2131.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2131_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2131_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2131_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_2131_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2131_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2131,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,3,0],[1,3,1],[1,3,2],[1,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[607,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2132","image_path":"images/combination3d_2132.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2132_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2132_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2132_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2132_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2132_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2132,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2]]],"total_cube_count":10}],"canvas_size":[555,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2133","image_path":"images/combination3d_2133.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2133_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2133_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2133_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2133_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2133_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2133,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":15}],"canvas_size":[608,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2134","image_path":"images/combination3d_2134.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2134_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2134_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2134_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2134_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2134_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2134,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,4,0],[0,4,1],[0,4,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,3,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[2,3,1],[2,3,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,2,0],[2,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,2],[2,0,0]]],"total_cube_count":14}],"canvas_size":[550,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2135","image_path":"images/combination3d_2135.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2135_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2135_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2135_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2135_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2135_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2135,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8}],"canvas_size":[571,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2136","image_path":"images/combination3d_2136.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2136_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2136_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2136_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_2136_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2136_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2136,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,2]],[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,1],[2,0,2]],[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[0,1,3],[1,0,3],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[2,1,3]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0]],[[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[587,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2137","image_path":"images/combination3d_2137.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2137_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2137_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2137_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2137_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2137_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2137,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,1,1],[3,0,1],[3,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[594,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2138","image_path":"images/combination3d_2138.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2138_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2138_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2138_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2138_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2138_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2138,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":8}],"canvas_size":[580,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2139","image_path":"images/combination3d_2139.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2139_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2139_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2139_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2139_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2139_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2139,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,0,0],[1,1,3]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[620,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2140","image_path":"images/combination3d_2140.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2140_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2140_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2140_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_2140_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2140_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2140,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,2],[2,1,2],[3,1,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[598,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2141","image_path":"images/combination3d_2141.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2141_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2141_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2141_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_2141_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2141_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2141,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[573,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2142","image_path":"images/combination3d_2142.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2142_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2142_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2142_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2142_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2142_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2142,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[616,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2143","image_path":"images/combination3d_2143.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2143_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2143_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2143_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2143_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2143_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2143,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":9}],"canvas_size":[602,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2144","image_path":"images/combination3d_2144.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2144_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2144_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2144_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2144_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2144_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2144,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,0,2],[2,1,2],[2,2,2],[2,2,3]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14}],"canvas_size":[598,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2145","image_path":"images/combination3d_2145.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2145_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2145_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2145_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2145_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2145_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2145,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[573,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2146","image_path":"images/combination3d_2146.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2146_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2146_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2146_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2146_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2146_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2146,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":12}],"canvas_size":[571,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2147","image_path":"images/combination3d_2147.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2147_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2147_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2147_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2147_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2147_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2147,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[599,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2148","image_path":"images/combination3d_2148.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2148_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2148_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2148_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_2148_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2148_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2148,"target_cube_count":8,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,3]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,2,1],[3,2,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,2],[3,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12}],"canvas_size":[550,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2149","image_path":"images/combination3d_2149.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2149_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2149_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2149_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2149_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2149_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2149,"target_cube_count":12,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10}],"canvas_size":[598,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2150","image_path":"images/combination3d_2150.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2150_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2150_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2150_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2150_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2150_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2150,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]]],"total_cube_count":11}],"canvas_size":[586,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2151","image_path":"images/combination3d_2151.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2151_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2151_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2151_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2151_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2151_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2151,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[612,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2152","image_path":"images/combination3d_2152.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2152_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2152_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2152_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2152_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2152_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2152,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,1,3],[0,2,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,0,5],[0,1,3]]],"total_cube_count":13}],"canvas_size":[562,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2153","image_path":"images/combination3d_2153.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2153_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2153_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2153_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2153_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2153_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2153,"target_cube_count":13,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[608,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2154","image_path":"images/combination3d_2154.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2154_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2154_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2154_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_2154_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2154_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2154,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13}],"canvas_size":[552,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2155","image_path":"images/combination3d_2155.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2155_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2155_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2155_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2155_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2155_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2155,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[605,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2156","image_path":"images/combination3d_2156.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2156_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2156_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2156_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2156_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2156_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2156,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,2,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[596,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2157","image_path":"images/combination3d_2157.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2157_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2157_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2157_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2157_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2157_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2157,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0],[4,0,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,2],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14}],"canvas_size":[620,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2158","image_path":"images/combination3d_2158.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2158_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2158_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2158_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2158_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2158_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2158,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[3,0,0],[4,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[590,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2159","image_path":"images/combination3d_2159.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2159_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2159_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2159_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2159_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2159_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2159,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,3]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[586,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2160","image_path":"images/combination3d_2160.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2160_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2160_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2160_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_2160_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2160_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2160,"target_cube_count":11,"target_cubes":[[0,2,0],[1,2,0],[2,2,0],[3,0,0],[3,0,1],[3,0,2],[3,1,0],[3,2,0],[3,2,1],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[2,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[614,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2161","image_path":"images/combination3d_2161.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2161_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2161_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2161_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2161_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2161_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2161,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[2,1,1]]],"total_cube_count":12}],"canvas_size":[620,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2162","image_path":"images/combination3d_2162.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2162_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2162_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2162_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2162_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2162_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2162,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,2,1]]],"total_cube_count":10}],"canvas_size":[617,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2163","image_path":"images/combination3d_2163.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2163_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2163_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2163_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2163_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2163_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2163,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[3,0,0],[3,1,0],[4,1,0],[4,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,2],[0,2,3],[0,3,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0],[4,1,0],[4,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[588,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2164","image_path":"images/combination3d_2164.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2164_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2164_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2164_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2164_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2164_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2164,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,0,0],[3,1,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,1,3],[0,2,1],[0,2,2],[0,3,0],[0,3,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,2,1],[1,3,1],[2,1,0],[2,1,1],[2,2,1],[3,0,1],[3,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[613,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2165","image_path":"images/combination3d_2165.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2165_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2165_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2165_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2165_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2165_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2165,"target_cube_count":11,"target_cubes":[[0,2,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,2,0],[5,2,0],[5,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8}],"canvas_size":[566,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2166","image_path":"images/combination3d_2166.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2166_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2166_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2166_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2166_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2166_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2166,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3]]],"total_cube_count":12}],"canvas_size":[564,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2167","image_path":"images/combination3d_2167.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2167_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2167_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2167_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_2167_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2167_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2167,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,1],[3,1,1],[4,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]]],"total_cube_count":14}],"canvas_size":[562,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2168","image_path":"images/combination3d_2168.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2168_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2168_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2168_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2168_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2168_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2168,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[592,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2169","image_path":"images/combination3d_2169.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2169_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2169_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2169_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2169_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2169_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2169,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1],[1,2,0],[1,2,1],[2,2,1],[2,3,0],[2,3,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[604,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2170","image_path":"images/combination3d_2170.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2170_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2170_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2170_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2170_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2170_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2170,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,2],[1,0,3],[2,0,3]]],"total_cube_count":14}],"canvas_size":[580,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2171","image_path":"images/combination3d_2171.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2171_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2171_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2171_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2171_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2171_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2171,"target_cube_count":14,"target_cubes":[[0,3,0],[0,3,1],[0,3,2],[1,3,0],[1,3,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,1,1],[1,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,2,0]]],"total_cube_count":10}],"canvas_size":[616,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2172","image_path":"images/combination3d_2172.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2172_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2172_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2172_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2172_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,6","question_id":"combination3d_2172_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2172,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1]],[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":13}],"canvas_size":[578,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2173","image_path":"images/combination3d_2173.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2173_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2173_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2173_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2173_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2173_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2173,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[556,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2174","image_path":"images/combination3d_2174.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2174_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2174_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2174_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2174_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2174_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2174,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[596,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2175","image_path":"images/combination3d_2175.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2175_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2175_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2175_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2175_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2175_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2175,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]],[[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,1],[1,1,1],[1,2,1],[1,3,1],[1,4,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]],[[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,1,2]]],"total_cube_count":14}],"canvas_size":[571,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2176","image_path":"images/combination3d_2176.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2176_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2176_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2176_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_2176_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2176_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2176,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[557,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2177","image_path":"images/combination3d_2177.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2177_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2177_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2177_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_2177_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2177_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2177,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,2],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,0,3],[1,1,2],[1,1,3],[1,2,3]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[556,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2178","image_path":"images/combination3d_2178.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2178_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2178_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2178_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2178_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2178_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2178,"target_cube_count":14,"target_cubes":[[0,2,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[2,3,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":15}],"canvas_size":[594,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2179","image_path":"images/combination3d_2179.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2179_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2179_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2179_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2179_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2179_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2179,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":12}],"canvas_size":[571,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2180","image_path":"images/combination3d_2180.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2180_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2180_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2180_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2180_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2180_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2180,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[568,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2181","image_path":"images/combination3d_2181.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2181_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2181_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2181_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2181_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2181_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2181,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,1]],[[0,0,1],[0,1,1],[0,2,1],[1,2,1],[1,3,0],[1,3,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":14}],"canvas_size":[585,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2182","image_path":"images/combination3d_2182.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2182_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2182_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2182_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2182_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2182_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2182,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[614,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2183","image_path":"images/combination3d_2183.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2183_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2183_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2183_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2183_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2183_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2183,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[555,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2184","image_path":"images/combination3d_2184.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2184_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2184_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2184_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2184_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2184_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2184,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,2],[1,0,1],[1,3,2]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,1],[1,1,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1],[3,2,0],[3,2,1],[3,2,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":15}],"canvas_size":[585,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2185","image_path":"images/combination3d_2185.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2185_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2185_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2185_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2185_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2185_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2185,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1],[2,4,2],[2,4,3],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1],[3,2,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,1],[2,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":14}],"canvas_size":[563,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2186","image_path":"images/combination3d_2186.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2186_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2186_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2186_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2186_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2186_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2186,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4],[1,2,5]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,4,1],[1,0,2],[1,1,0],[1,1,2],[1,2,0],[1,2,2],[1,3,0],[1,3,2],[1,4,0],[1,4,1],[1,4,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":13}],"canvas_size":[565,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2187","image_path":"images/combination3d_2187.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2187_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2187_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2187_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2187_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2187_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2187,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,2],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[587,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2188","image_path":"images/combination3d_2188.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2188_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2188_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2188_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2188_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2188_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2188,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[1,3,2]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[559,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2189","image_path":"images/combination3d_2189.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2189_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2189_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2189_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2189_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2189_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2189,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[1,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[596,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2190","image_path":"images/combination3d_2190.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2190_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2190_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2190_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_2190_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2190_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2190,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[571,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2191","image_path":"images/combination3d_2191.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2191_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2191_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2191_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2191_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2191_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2191,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[596,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2192","image_path":"images/combination3d_2192.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2192_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2192_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2192_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2192_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2192_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2192,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,3,1],[1,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,1,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[616,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2193","image_path":"images/combination3d_2193.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2193_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2193_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2193_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2193_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2193_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2193,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[3,3,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[599,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2194","image_path":"images/combination3d_2194.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2194_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2194_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2194_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2194_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2194_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2194,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[580,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2195","image_path":"images/combination3d_2195.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2195_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2195_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2195_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2195_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2195_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2195,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[563,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2196","image_path":"images/combination3d_2196.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2196_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2196_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2196_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2196_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2196_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2196,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[561,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2197","image_path":"images/combination3d_2197.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2197_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2197_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2197_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2197_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2197_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2197,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9}],"canvas_size":[552,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2198","image_path":"images/combination3d_2198.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2198_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2198_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2198_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2198_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2198_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2198,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[614,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2199","image_path":"images/combination3d_2199.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2199_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2199_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2199_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2199_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2199_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2199,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,3,2],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[3,0,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[593,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2200","image_path":"images/combination3d_2200.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2200_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2200_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2200_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2200_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2200_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2200,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,1,3],[1,2,1]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[570,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2201","image_path":"images/combination3d_2201.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2201_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2201_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2201_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2201_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2201_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2201,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,2,0],[3,0,0],[3,2,0],[4,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,1],[2,0,2],[2,0,3],[2,0,4]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[3,0,1],[3,0,2],[3,0,3],[3,0,4]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,2],[1,1,3]]],"total_cube_count":14}],"canvas_size":[552,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2202","image_path":"images/combination3d_2202.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2202_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2202_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2202_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_2202_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2202_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2202,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[3,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[618,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2203","image_path":"images/combination3d_2203.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2203_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2203_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2203_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2203_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2203_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2203,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,1,1],[2,2,1],[2,2,2],[2,3,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,2],[0,1,2],[1,0,2],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2],[4,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[556,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2204","image_path":"images/combination3d_2204.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2204_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2204_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2204_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2204_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2204_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2204,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[565,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2205","image_path":"images/combination3d_2205.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2205_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2205_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2205_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2205_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_2205_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2205,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,2,3]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[606,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2206","image_path":"images/combination3d_2206.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2206_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2206_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2206_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2206_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2206_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2206,"target_cube_count":11,"target_cubes":[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[585,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2207","image_path":"images/combination3d_2207.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2207_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2207_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2207_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2207_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2207_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2207,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[2,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":9}],"canvas_size":[565,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2208","image_path":"images/combination3d_2208.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2208_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2208_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2208_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_2208_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2208_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2208,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,1],[3,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[558,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2209","image_path":"images/combination3d_2209.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2209_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2209_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2209_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2209_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2209_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2209,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[563,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2210","image_path":"images/combination3d_2210.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2210_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2210_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2210_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2210_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2210_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2210,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,3],[1,1,1],[1,1,2]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[614,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2211","image_path":"images/combination3d_2211.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2211_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2211_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2211_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2211_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2211_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2211,"target_cube_count":13,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[615,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2212","image_path":"images/combination3d_2212.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2212_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2212_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2212_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2212_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2212_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2212,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,3,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[3,3,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,1],[1,0,3],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,3]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2]],[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":12}],"canvas_size":[588,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2213","image_path":"images/combination3d_2213.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2213_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2213_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2213_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2213_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2213_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2213,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,3,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,3,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[4,0,0]]],"total_cube_count":11}],"canvas_size":[585,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2214","image_path":"images/combination3d_2214.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2214_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2214_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2214_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2214_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2214_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2214,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[1,0,1],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":12}],"canvas_size":[578,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2215","image_path":"images/combination3d_2215.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2215_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2215_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2215_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2215_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2215_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2215,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[592,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2216","image_path":"images/combination3d_2216.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2216_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2216_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2216_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2216_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2216_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2216,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[572,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2217","image_path":"images/combination3d_2217.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2217_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2217_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2217_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2217_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2217_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2217,"target_cube_count":8,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,2,0],[3,2,0],[3,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,3],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,1,3],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[560,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2218","image_path":"images/combination3d_2218.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2218_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2218_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2218_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_2218_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2218_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2218,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10}],"canvas_size":[559,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2219","image_path":"images/combination3d_2219.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2219_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2219_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2219_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2219_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2219_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2219,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0],[2,2,1],[2,3,0],[3,2,0],[4,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,2,2],[0,3,2],[0,4,2],[1,2,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0],[2,2,1],[3,2,0],[4,2,0]]],"total_cube_count":12}],"canvas_size":[610,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2220","image_path":"images/combination3d_2220.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2220_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2220_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2220_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2220_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2220_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2220,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,3],[1,0,2],[1,0,3],[1,0,4],[1,1,3],[1,1,4],[2,0,0],[2,0,1],[2,0,2],[2,0,3]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,2],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,2,2],[2,2,3]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0]]],"total_cube_count":15}],"canvas_size":[613,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2221","image_path":"images/combination3d_2221.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2221_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2221_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2221_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2221_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2221_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2221,"target_cube_count":14,"target_cubes":[[0,3,0],[0,3,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,4,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8}],"canvas_size":[577,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2222","image_path":"images/combination3d_2222.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2222_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2222_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2222_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2222_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2222_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2222,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,3,0],[0,3,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8}],"canvas_size":[584,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2223","image_path":"images/combination3d_2223.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2223_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2223_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2223_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2223_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2223_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2223,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,1,0],[0,1,1],[1,0,2],[1,1,1],[1,1,2],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[572,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2224","image_path":"images/combination3d_2224.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2224_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2224_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2224_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2224_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2224_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2224,"target_cube_count":12,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[573,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2225","image_path":"images/combination3d_2225.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2225_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2225_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2225_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2225_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2225_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2225,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,2,0],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":14}],"canvas_size":[560,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2226","image_path":"images/combination3d_2226.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2226_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2226_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2226_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2226_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2226_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2226,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[584,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2227","image_path":"images/combination3d_2227.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2227_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2227_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2227_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2227_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2227_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2227,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":10}],"canvas_size":[586,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2228","image_path":"images/combination3d_2228.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2228_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2228_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2228_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2228_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,6","question_id":"combination3d_2228_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2228,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,1],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,0,2]],[[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[606,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2229","image_path":"images/combination3d_2229.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2229_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2229_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2229_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2229_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2229_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2229,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,1]]],"total_cube_count":10}],"canvas_size":[571,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2230","image_path":"images/combination3d_2230.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2230_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2230_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2230_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2230_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2230_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2230,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[3,1,1],[4,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[553,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2231","image_path":"images/combination3d_2231.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2231_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2231_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2231_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2231_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2231_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2231,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":12}],"canvas_size":[554,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2232","image_path":"images/combination3d_2232.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2232_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2232_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2232_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2232_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2232_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2232,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8}],"canvas_size":[614,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2233","image_path":"images/combination3d_2233.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2233_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2233_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2233_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2233_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2233_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2233,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[560,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2234","image_path":"images/combination3d_2234.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2234_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2234_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2234_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2234_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2234_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2234,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,1],[2,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,1],[0,2,2],[1,2,0],[1,2,2],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[583,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2235","image_path":"images/combination3d_2235.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2235_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2235_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2235_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2235_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2235_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2235,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,4],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[620,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2236","image_path":"images/combination3d_2236.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2236_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2236_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2236_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2236_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2236_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2236,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,1,1],[1,2,1],[2,2,1],[3,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[557,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2237","image_path":"images/combination3d_2237.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2237_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2237_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2237_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_2237_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2237_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2237,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[3,3,0],[3,4,0],[3,4,1],[3,4,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[3,3,0],[3,4,0],[3,4,1],[3,4,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[2,2,2],[2,2,3],[3,0,4],[3,1,4],[3,2,3],[3,2,4]]],"total_cube_count":13}],"canvas_size":[574,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2238","image_path":"images/combination3d_2238.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2238_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2238_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2238_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2238_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2238_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2238,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[3,3,0],[3,4,0],[3,4,1],[3,4,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[582,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2239","image_path":"images/combination3d_2239.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2239_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2239_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2239_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2239_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2239_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2239,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12}],"canvas_size":[586,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2240","image_path":"images/combination3d_2240.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2240_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2240_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2240_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2240_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2240_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2240,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1],[3,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[3,1,1],[3,1,2],[3,1,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,3,1],[1,1,1],[1,2,1],[1,3,1],[2,3,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,1,1],[1,1,1],[2,0,0],[2,0,1],[2,1,1],[2,2,1],[3,1,1],[3,2,0],[3,2,1]]],"total_cube_count":14}],"canvas_size":[613,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2241","image_path":"images/combination3d_2241.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2241_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2241_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2241_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2241_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2241_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2241,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,3,0],[3,2,0],[3,2,1],[3,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,1,2],[2,0,1],[2,0,2],[2,1,2]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[4,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14}],"canvas_size":[614,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2242","image_path":"images/combination3d_2242.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2242_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2242_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2242_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_2242_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2242_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2242,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[606,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2243","image_path":"images/combination3d_2243.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2243_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2243_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2243_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2243_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2243_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2243,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[620,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2244","image_path":"images/combination3d_2244.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2244_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2244_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2244_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2244_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2244_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2244,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[567,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2245","image_path":"images/combination3d_2245.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2245_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2245_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2245_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_2245_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2245_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2245,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":15}],"canvas_size":[555,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2246","image_path":"images/combination3d_2246.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2246_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2246_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2246_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2246_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2246_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2246,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,0,2],[1,2,1],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,1,1],[1,1,2],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[551,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2247","image_path":"images/combination3d_2247.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2247_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2247_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2247_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2247_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2247_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2247,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[587,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2248","image_path":"images/combination3d_2248.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2248_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2248_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2248_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2248_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2248_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2248,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,2,2]],[[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,2,2]]],"total_cube_count":13}],"canvas_size":[590,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2249","image_path":"images/combination3d_2249.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2249_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2249_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2249_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2249_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2249_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2249,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2],[3,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[610,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2250","image_path":"images/combination3d_2250.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2250_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2250_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2250_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2250_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2250_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2250,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[555,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2251","image_path":"images/combination3d_2251.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2251_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2251_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2251_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2251_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2251_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2251,"target_cube_count":10,"target_cubes":[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[569,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2252","image_path":"images/combination3d_2252.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2252_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2252_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2252_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2252_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2252_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2252,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,2,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[608,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2253","image_path":"images/combination3d_2253.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2253_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2253_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2253_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2253_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2253_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2253,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,1,1]]],"total_cube_count":14}],"canvas_size":[573,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2254","image_path":"images/combination3d_2254.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2254_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2254_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2254_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_2254_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2254_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2254,"target_cube_count":14,"target_cubes":[[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15}],"canvas_size":[551,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2255","image_path":"images/combination3d_2255.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2255_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2255_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2255_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_2255_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2255_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2255,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[2,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[1,3,0],[1,3,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0],[4,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0]]],"total_cube_count":12}],"canvas_size":[564,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2256","image_path":"images/combination3d_2256.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2256_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2256_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2256_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2256_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2256_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2256,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[554,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2257","image_path":"images/combination3d_2257.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2257_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2257_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2257_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2257_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2257_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2257,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,1],[2,1,2],[3,1,2]]],"total_cube_count":13}],"canvas_size":[558,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2258","image_path":"images/combination3d_2258.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2258_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2258_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2258_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2258_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2258_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2258,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[563,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2259","image_path":"images/combination3d_2259.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2259_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2259_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2259_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2259_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2259_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2259,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,0,2],[2,1,1],[3,0,1],[3,0,2],[3,1,1],[4,1,0],[4,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,3,0],[0,3,1],[0,4,1],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[4,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[583,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2260","image_path":"images/combination3d_2260.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2260_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2260_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2260_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2260_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_2260_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2260,"target_cube_count":14,"target_cubes":[[0,3,0],[0,3,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[3,0,1],[4,0,1]]],"total_cube_count":12}],"canvas_size":[588,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2261","image_path":"images/combination3d_2261.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2261_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2261_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2261_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2261_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2261_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2261,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[0,2,1],[0,2,2],[0,3,1],[1,0,2],[1,1,2],[1,2,2],[1,3,1],[2,3,1]]],"total_cube_count":11}],"canvas_size":[576,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2262","image_path":"images/combination3d_2262.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2262_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2262_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2262_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2262_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2262_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2262,"target_cube_count":11,"target_cubes":[[0,2,0],[0,3,0],[0,4,0],[0,4,1],[0,5,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,2],[1,0,1],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,1],[2,1,2]]],"total_cube_count":11}],"canvas_size":[556,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2263","image_path":"images/combination3d_2263.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2263_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2263_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2263_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2263_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2263_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2263,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,5,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[0,2,5],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[1,0,2],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,5,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[555,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2264","image_path":"images/combination3d_2264.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2264_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2264_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2264_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2264_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2264_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2264,"target_cube_count":13,"target_cubes":[[0,3,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1],[2,5,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,1],[2,0,1]]],"total_cube_count":10}],"canvas_size":[556,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2265","image_path":"images/combination3d_2265.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2265_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2265_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2265_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2265_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2265_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2265,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9}],"canvas_size":[554,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2266","image_path":"images/combination3d_2266.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2266_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2266_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2266_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2266_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2266_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2266,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,1,2]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,1],[3,2,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14}],"canvas_size":[618,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2267","image_path":"images/combination3d_2267.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2267_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2267_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2267_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2267_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2267_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2267,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,1,2],[3,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[3,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0],[3,2,0]]],"total_cube_count":10}],"canvas_size":[571,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2268","image_path":"images/combination3d_2268.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2268_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2268_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2268_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2268_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2268_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2268,"target_cube_count":10,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,3,0],[3,3,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,3,1],[2,2,1],[2,3,0],[2,3,1],[3,1,1],[3,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[587,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2269","image_path":"images/combination3d_2269.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2269_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2269_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2269_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2269_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2269_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2269,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1]]],"total_cube_count":12}],"canvas_size":[585,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2270","image_path":"images/combination3d_2270.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2270_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2270_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2270_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2270_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2270_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2270,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,1],[2,1,1],[3,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1]]],"total_cube_count":11}],"canvas_size":[604,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2271","image_path":"images/combination3d_2271.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2271_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2271_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2271_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2271_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2271_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2271,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9}],"canvas_size":[584,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2272","image_path":"images/combination3d_2272.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2272_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2272_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2272_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2272_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2272_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2272,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[564,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2273","image_path":"images/combination3d_2273.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2273_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2273_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2273_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2273_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2273_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2273,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,0,2],[2,1,2],[2,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[551,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2274","image_path":"images/combination3d_2274.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2274_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2274_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2274_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2274_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2274_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2274,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1],[1,1,2],[1,2,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11}],"canvas_size":[597,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2275","image_path":"images/combination3d_2275.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2275_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2275_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2275_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2275_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2275_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2275,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,2],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[600,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2276","image_path":"images/combination3d_2276.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2276_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2276_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2276_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2276_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2276_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2276,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,0,2],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[1,0,1],[1,0,2],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[594,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2277","image_path":"images/combination3d_2277.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2277_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2277_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2277_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2277_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2277_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2277,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":9}],"canvas_size":[568,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2278","image_path":"images/combination3d_2278.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2278_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2278_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2278_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2278_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_2278_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2278,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":12}],"canvas_size":[607,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2279","image_path":"images/combination3d_2279.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2279_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2279_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2279_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2279_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2279_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2279,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[597,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2280","image_path":"images/combination3d_2280.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2280_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2280_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2280_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2280_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2280_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2280,"target_cube_count":8,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,1,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":13}],"canvas_size":[590,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2281","image_path":"images/combination3d_2281.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2281_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2281_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2281_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2281_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2281_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2281,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":8}],"canvas_size":[571,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2282","image_path":"images/combination3d_2282.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2282_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2282_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2282_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2282_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2282_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2282,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[1,0,1],[1,1,1],[1,1,2],[1,1,3]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":15}],"canvas_size":[559,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2283","image_path":"images/combination3d_2283.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2283_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2283_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2283_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2283_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2283_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2283,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,1],[1,2,1],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[595,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2284","image_path":"images/combination3d_2284.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2284_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2284_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2284_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2284_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2284_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2284,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,1,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,2,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,0,0]]],"total_cube_count":13}],"canvas_size":[588,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2285","image_path":"images/combination3d_2285.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2285_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2285_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2285_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2285_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2285_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2285,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9}],"canvas_size":[598,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2286","image_path":"images/combination3d_2286.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2286_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2286_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2286_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2286_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2286_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2286,"target_cube_count":9,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[0,3,1],[0,3,2]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[569,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2287","image_path":"images/combination3d_2287.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2287_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2287_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2287_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2287_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2287_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2287,"target_cube_count":11,"target_cubes":[[0,2,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[595,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2288","image_path":"images/combination3d_2288.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2288_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2288_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2288_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2288_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2288_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2288,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[614,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2289","image_path":"images/combination3d_2289.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2289_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2289_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2289_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2289_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2289_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2289,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[1,4,0],[1,4,1],[1,4,2]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[1,2,1],[1,4,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2],[0,1,3],[1,0,1],[1,0,2],[1,1,2],[2,1,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[617,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2290","image_path":"images/combination3d_2290.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2290_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2290_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2290_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2290_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2290_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2290,"target_cube_count":13,"target_cubes":[[0,3,0],[0,3,1],[0,4,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,5,0],[1,5,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[558,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2291","image_path":"images/combination3d_2291.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2291_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2291_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2291_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_2291_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2291_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2291,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,1],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,1,0],[1,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[588,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2292","image_path":"images/combination3d_2292.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2292_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2292_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2292_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2292_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2292_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2292,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1],[2,2,1]]],"total_cube_count":11}],"canvas_size":[608,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2293","image_path":"images/combination3d_2293.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2293_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2293_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2293_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2293_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2293_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2293,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[3,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":11}],"canvas_size":[580,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2294","image_path":"images/combination3d_2294.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2294_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2294_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2294_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2294_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2294_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2294,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":12}],"canvas_size":[585,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2295","image_path":"images/combination3d_2295.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2295_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2295_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2295_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2295_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2295_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2295,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1],[1,2,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8}],"canvas_size":[613,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2296","image_path":"images/combination3d_2296.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2296_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2296_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2296_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2296_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2296_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2296,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1]]],"total_cube_count":13}],"canvas_size":[609,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2297","image_path":"images/combination3d_2297.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2297_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2297_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2297_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2297_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2297_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2297,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[586,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2298","image_path":"images/combination3d_2298.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2298_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2298_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2298_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2298_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2298_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2298,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[2,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[569,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2299","image_path":"images/combination3d_2299.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2299_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2299_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2299_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2299_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2299_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2299,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":10}],"canvas_size":[610,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2300","image_path":"images/combination3d_2300.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2300_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2300_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2300_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2300_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2300_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2300,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":11}],"canvas_size":[588,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2301","image_path":"images/combination3d_2301.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2301_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2301_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2301_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_2301_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2301_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2301,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":8}],"canvas_size":[559,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2302","image_path":"images/combination3d_2302.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2302_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2302_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2302_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2302_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2302_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2302,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[565,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2303","image_path":"images/combination3d_2303.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2303_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2303_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2303_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2303_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_2303_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2303,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[620,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2304","image_path":"images/combination3d_2304.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2304_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2304_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2304_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2304_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2304_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2304,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13}],"canvas_size":[573,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2305","image_path":"images/combination3d_2305.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2305_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2305_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2305_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2305_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2305_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2305,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,3,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[3,0,0]]],"total_cube_count":9}],"canvas_size":[611,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2306","image_path":"images/combination3d_2306.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2306_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2306_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2306_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2306_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2306_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2306,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[2,0,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[1,2,1],[2,0,2],[2,1,1],[2,1,2],[3,0,1],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":12}],"canvas_size":[587,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2307","image_path":"images/combination3d_2307.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2307_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2307_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2307_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2307_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2307_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2307,"target_cube_count":11,"target_cubes":[[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1],[1,0,2],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[607,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2308","image_path":"images/combination3d_2308.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2308_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2308_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2308_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2308_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2308_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2308,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,1,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[584,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2309","image_path":"images/combination3d_2309.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2309_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2309_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2309_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2309_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_2309_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2309,"target_cube_count":14,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[588,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2310","image_path":"images/combination3d_2310.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2310_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2310_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2310_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2310_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2310_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2310,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,4,1],[0,4,2],[1,1,0],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,0]]],"total_cube_count":11}],"canvas_size":[569,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2311","image_path":"images/combination3d_2311.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2311_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2311_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2311_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2311_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2311_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2311,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,1],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[2,0,2],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,1],[2,1,1],[2,2,1],[2,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[610,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2312","image_path":"images/combination3d_2312.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2312_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2312_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2312_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2312_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2312_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2312,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,2,1],[2,3,0],[2,4,0],[3,2,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8}],"canvas_size":[606,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2313","image_path":"images/combination3d_2313.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2313_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2313_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2313_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2313_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2313_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2313,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[1,3,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11}],"canvas_size":[574,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2314","image_path":"images/combination3d_2314.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2314_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2314_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2314_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_2314_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2314_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2314,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9}],"canvas_size":[584,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2315","image_path":"images/combination3d_2315.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2315_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2315_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2315_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2315_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2315_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2315,"target_cube_count":8,"target_cubes":[[0,2,0],[1,2,0],[1,2,1],[2,2,0],[3,2,0],[4,0,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":13}],"canvas_size":[608,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2316","image_path":"images/combination3d_2316.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2316_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2316_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2316_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2316_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2316_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2316,"target_cube_count":13,"target_cubes":[[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[1,4,1],[2,4,0],[2,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[599,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2317","image_path":"images/combination3d_2317.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2317_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2317_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2317_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2317_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2317_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2317,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,1,1],[1,2,1],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[563,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2318","image_path":"images/combination3d_2318.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2318_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2318_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2318_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2318_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2318_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2318,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0]]],"total_cube_count":8}],"canvas_size":[565,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2319","image_path":"images/combination3d_2319.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2319_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2319_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2319_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2319_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2319_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2319,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[612,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2320","image_path":"images/combination3d_2320.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2320_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2320_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2320_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2320_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2320_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2320,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[594,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2321","image_path":"images/combination3d_2321.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2321_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2321_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2321_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_2321_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2321_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2321,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,1]]],"total_cube_count":11}],"canvas_size":[560,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2322","image_path":"images/combination3d_2322.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2322_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2322_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2322_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2322_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2322_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2322,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,1]]],"total_cube_count":9}],"canvas_size":[600,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2323","image_path":"images/combination3d_2323.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2323_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2323_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2323_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2323_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2323_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2323,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,2],[2,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[618,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2324","image_path":"images/combination3d_2324.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2324_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2324_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2324_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2324_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2324_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2324,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[616,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2325","image_path":"images/combination3d_2325.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2325_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2325_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2325_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2325_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2325_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2325,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,0,2],[2,1,1]]],"total_cube_count":12}],"canvas_size":[603,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2326","image_path":"images/combination3d_2326.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2326_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2326_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2326_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2326_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2326_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2326,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,2],[0,3,0],[0,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[575,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2327","image_path":"images/combination3d_2327.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2327_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2327_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2327_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2327_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2327_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2327,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1],[1,1,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":11}],"canvas_size":[577,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2328","image_path":"images/combination3d_2328.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2328_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2328_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2328_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2328_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2328_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2328,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[575,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2329","image_path":"images/combination3d_2329.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2329_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2329_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2329_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2329_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2329_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2329,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[585,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2330","image_path":"images/combination3d_2330.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2330_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2330_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2330_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2330_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2330_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2330,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,2],[1,0,3],[2,0,3]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,2],[2,0,1],[2,1,1],[2,2,1],[3,1,0],[3,1,1],[3,2,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[585,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2331","image_path":"images/combination3d_2331.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2331_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2331_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2331_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2331_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2331_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2331,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,1]],[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[3,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[571,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2332","image_path":"images/combination3d_2332.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2332_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2332_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2332_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2332_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2332_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2332,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[3,2,0],[3,2,1],[3,2,2],[3,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,1,1]]],"total_cube_count":10}],"canvas_size":[554,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2333","image_path":"images/combination3d_2333.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2333_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2333_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2333_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2333_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2333_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2333,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,5,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,2,2],[1,3,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":15}],"canvas_size":[590,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2334","image_path":"images/combination3d_2334.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2334_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2334_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2334_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_2334_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2334_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2334,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,3,0],[2,3,1],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,2],[1,2,1],[1,2,2],[2,2,0],[2,2,1],[3,0,1],[3,1,1],[3,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[2,1,1]]],"total_cube_count":13}],"canvas_size":[593,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2335","image_path":"images/combination3d_2335.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2335_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2335_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2335_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2335_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2335_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2335,"target_cube_count":13,"target_cubes":[[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,1,1],[1,2,1],[1,3,1],[2,1,1],[2,2,0],[2,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[1,1,3],[2,1,1],[2,1,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]]],"total_cube_count":12}],"canvas_size":[608,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2336","image_path":"images/combination3d_2336.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2336_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2336_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2336_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2336_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2336_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2336,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]],[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,2,1],[0,2,2],[0,3,1],[1,0,0],[1,0,1],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,0,1],[1,2,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[582,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2337","image_path":"images/combination3d_2337.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2337_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2337_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2337_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2337_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2337_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2337,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,1]]],"total_cube_count":12}],"canvas_size":[616,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2338","image_path":"images/combination3d_2338.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2338_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2338_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2338_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2338_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2338_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2338,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,1,0],[4,0,0],[4,0,1],[4,0,2],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,2,1],[3,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[560,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2339","image_path":"images/combination3d_2339.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2339_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2339_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2339_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2339_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2339_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2339,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,1],[0,1,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[571,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2340","image_path":"images/combination3d_2340.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2340_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2340_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2340_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2340_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2340_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2340,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,2,1],[3,2,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[618,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2341","image_path":"images/combination3d_2341.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2341_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2341_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2341_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2341_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2341_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2341,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[576,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2342","image_path":"images/combination3d_2342.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2342_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2342_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2342_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2342_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2342_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2342,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[0,4,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0]]],"total_cube_count":15}],"canvas_size":[615,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2343","image_path":"images/combination3d_2343.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2343_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2343_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2343_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2343_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2343_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2343,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[3,0,0],[4,0,0],[4,0,1],[5,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":10}],"canvas_size":[598,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2344","image_path":"images/combination3d_2344.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2344_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2344_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2344_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2344_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2344_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2344,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11}],"canvas_size":[616,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2345","image_path":"images/combination3d_2345.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2345_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2345_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2345_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2345_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2345_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2345,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[599,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2346","image_path":"images/combination3d_2346.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2346_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2346_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2346_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2346_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2346_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2346,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0],[2,2,0],[2,3,0],[2,3,1],[3,2,0],[3,3,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,1],[1,0,2],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,1],[1,0,2],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,0],[3,0,1],[3,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[576,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2347","image_path":"images/combination3d_2347.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2347_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2347_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2347_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2347_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2347_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2347,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[570,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2348","image_path":"images/combination3d_2348.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2348_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2348_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2348_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2348_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2348_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2348,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[595,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2349","image_path":"images/combination3d_2349.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2349_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2349_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2349_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2349_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2349_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2349,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[614,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2350","image_path":"images/combination3d_2350.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2350_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2350_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2350_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2350_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2350_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2350,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]]],"total_cube_count":12}],"canvas_size":[610,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2351","image_path":"images/combination3d_2351.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2351_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2351_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2351_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_2351_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2351_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2351,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12}],"canvas_size":[602,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2352","image_path":"images/combination3d_2352.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2352_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2352_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2352_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2352_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2352_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2352,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,3],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,1,1],[0,2,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,1,0],[2,1,1]]],"total_cube_count":13}],"canvas_size":[580,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2353","image_path":"images/combination3d_2353.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2353_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2353_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2353_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2353_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2353_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2353,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,0,0],[2,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[3,0,1]]],"total_cube_count":14}],"canvas_size":[600,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2354","image_path":"images/combination3d_2354.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2354_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2354_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2354_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_2354_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2354_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2354,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[587,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2355","image_path":"images/combination3d_2355.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2355_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2355_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2355_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2355_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2355_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2355,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,1],[1,3,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[598,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2356","image_path":"images/combination3d_2356.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2356_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2356_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2356_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2356_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2356_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2356,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[592,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2357","image_path":"images/combination3d_2357.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2357_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2357_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2357_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2357_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2357_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2357,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":13}],"canvas_size":[609,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2358","image_path":"images/combination3d_2358.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2358_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2358_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2358_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2358_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2358_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2358,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[0,3,1],[0,3,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[560,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2359","image_path":"images/combination3d_2359.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2359_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2359_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2359_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2359_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2359_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2359,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,1,0],[3,2,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,1],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[609,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2360","image_path":"images/combination3d_2360.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2360_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2360_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2360_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2360_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2360_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2360,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[0,4,0],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[1,4,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[585,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2361","image_path":"images/combination3d_2361.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2361_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2361_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2361_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2361_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_2361_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2361,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,2],[3,1,2],[3,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[1,4,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[619,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2362","image_path":"images/combination3d_2362.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2362_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2362_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2362_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_2362_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2362_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2362,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[617,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2363","image_path":"images/combination3d_2363.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2363_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2363_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2363_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_2363_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2363_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2363,"target_cube_count":9,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[586,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2364","image_path":"images/combination3d_2364.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2364_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2364_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2364_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2364_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2364_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2364,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[3,1,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":12}],"canvas_size":[561,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2365","image_path":"images/combination3d_2365.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2365_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2365_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2365_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2365_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2365_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2365,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,4,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,2],[3,0,1],[3,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[597,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2366","image_path":"images/combination3d_2366.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2366_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2366_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2366_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_2366_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2366_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2366,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,2],[1,1,2],[1,2,2],[2,0,2],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[598,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2367","image_path":"images/combination3d_2367.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2367_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2367_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2367_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2367_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2367_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2367,"target_cube_count":13,"target_cubes":[[0,3,0],[0,3,1],[0,3,2],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[2,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[594,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2368","image_path":"images/combination3d_2368.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2368_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2368_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2368_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2368_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2368_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2368,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,3,1],[0,3,2],[1,1,1],[1,2,1],[2,1,1],[2,1,2],[2,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":15}],"canvas_size":[599,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2369","image_path":"images/combination3d_2369.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2369_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2369_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2369_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_2369_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2369_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2369,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[599,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2370","image_path":"images/combination3d_2370.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2370_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2370_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2370_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2370_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2370_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2370,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,2,1],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12}],"canvas_size":[614,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2371","image_path":"images/combination3d_2371.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2371_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2371_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2371_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2371_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2371_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2371,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[615,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2372","image_path":"images/combination3d_2372.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2372_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2372_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2372_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2372_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2372_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2372,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[601,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2373","image_path":"images/combination3d_2373.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2373_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2373_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2373_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2373_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2373_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2373,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[592,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2374","image_path":"images/combination3d_2374.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2374_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2374_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2374_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2374_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2374_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2374,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10}],"canvas_size":[583,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2375","image_path":"images/combination3d_2375.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2375_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2375_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2375_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2375_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2375_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2375,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,3],[0,1,4],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,3],[2,1,4]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,4,0],[3,3,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,1,2],[1,1,2],[2,1,2],[3,0,2],[3,1,0],[3,1,1],[3,1,2],[4,0,1],[4,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,4,0]]],"total_cube_count":13}],"canvas_size":[616,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2376","image_path":"images/combination3d_2376.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2376_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2376_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2376_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2376_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2376_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2376,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[609,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2377","image_path":"images/combination3d_2377.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2377_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2377_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2377_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2377_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2377_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2377,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,3]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[565,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2378","image_path":"images/combination3d_2378.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2378_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2378_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2378_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2378_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2378_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2378,"target_cube_count":10,"target_cubes":[[0,4,0],[0,4,1],[0,4,2],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":9}],"canvas_size":[575,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2379","image_path":"images/combination3d_2379.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2379_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2379_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2379_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2379_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2379_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2379,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,1],[1,2,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[603,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2380","image_path":"images/combination3d_2380.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2380_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2380_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2380_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_2380_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2380_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2380,"target_cube_count":9,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[3,0,1],[3,1,1],[3,1,2],[4,0,0],[4,0,1],[4,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14}],"canvas_size":[577,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2381","image_path":"images/combination3d_2381.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2381_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2381_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2381_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2381_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2381_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2381,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,3,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[613,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2382","image_path":"images/combination3d_2382.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2382_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2382_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2382_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_2382_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2382_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2382,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[603,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2383","image_path":"images/combination3d_2383.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2383_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2383_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2383_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2383_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2383_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2383,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":9}],"canvas_size":[599,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2384","image_path":"images/combination3d_2384.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2384_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2384_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2384_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2384_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2384_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2384,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[611,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2385","image_path":"images/combination3d_2385.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2385_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2385_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2385_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2385_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2385_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2385,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":9}],"canvas_size":[603,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2386","image_path":"images/combination3d_2386.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2386_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2386_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2386_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2386_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2386_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2386,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":9}],"canvas_size":[551,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2387","image_path":"images/combination3d_2387.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2387_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2387_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2387_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2387_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2387_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2387,"target_cube_count":9,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1],[2,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14}],"canvas_size":[571,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2388","image_path":"images/combination3d_2388.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2388_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2388_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2388_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2388_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2388_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2388,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,2,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1]]],"total_cube_count":10}],"canvas_size":[576,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2389","image_path":"images/combination3d_2389.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2389_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2389_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2389_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2389_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2389_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2389,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":9}],"canvas_size":[612,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2390","image_path":"images/combination3d_2390.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2390_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2390_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2390_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2390_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2390_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2390,"target_cube_count":8,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,2,0],[0,2,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[1,3,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,1]]],"total_cube_count":10}],"canvas_size":[578,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2391","image_path":"images/combination3d_2391.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2391_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2391_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2391_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2391_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2391_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2391,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,2],[0,0,3],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[587,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2392","image_path":"images/combination3d_2392.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2392_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2392_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2392_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_2392_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2392_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2392,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,1],[3,2,0],[3,2,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,0,5],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[4,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,2],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[555,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2393","image_path":"images/combination3d_2393.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2393_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2393_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2393_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2393_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2393_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2393,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":11}],"canvas_size":[607,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2394","image_path":"images/combination3d_2394.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2394_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2394_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2394_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2394_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2394_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2394,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,2,1],[1,2,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,1,1],[2,0,1],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2]]],"total_cube_count":15}],"canvas_size":[615,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2395","image_path":"images/combination3d_2395.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2395_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2395_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2395_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2395_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_2395_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2395,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[617,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2396","image_path":"images/combination3d_2396.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2396_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2396_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2396_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2396_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2396_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2396,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0],[4,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0],[4,1,1],[4,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,3,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,2,1],[0,2,2],[1,1,4]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[559,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2397","image_path":"images/combination3d_2397.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2397_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2397_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2397_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_2397_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2397_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2397,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[4,0,0],[4,1,0],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[586,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2398","image_path":"images/combination3d_2398.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2398_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2398_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2398_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2398_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2398_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2398,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0]]],"total_cube_count":9}],"canvas_size":[591,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2399","image_path":"images/combination3d_2399.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2399_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2399_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2399_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_2399_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2399_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2399,"target_cube_count":9,"target_cubes":[[0,2,0],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,3,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":11}],"canvas_size":[558,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2400","image_path":"images/combination3d_2400.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2400_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2400_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2400_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2400_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2400_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2400,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[0,4,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[556,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2401","image_path":"images/combination3d_2401.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2401_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2401_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2401_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_2401_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2401_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2401,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[0,3,4],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[559,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2402","image_path":"images/combination3d_2402.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2402_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2402_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2402_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2402_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2402_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2402,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[560,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2403","image_path":"images/combination3d_2403.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2403_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2403_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2403_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_2403_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2403_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2403,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[605,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2404","image_path":"images/combination3d_2404.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2404_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2404_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2404_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2404_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2404_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2404,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":11}],"canvas_size":[581,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2405","image_path":"images/combination3d_2405.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2405_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2405_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2405_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2405_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2405_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2405,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1],[3,1,2],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,2],[1,1,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,2]]],"total_cube_count":10}],"canvas_size":[603,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2406","image_path":"images/combination3d_2406.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2406_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2406_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2406_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2406_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2406_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2406,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1],[3,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[598,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2407","image_path":"images/combination3d_2407.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2407_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2407_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2407_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2407_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2407_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2407,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":10}],"canvas_size":[599,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2408","image_path":"images/combination3d_2408.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2408_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2408_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2408_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2408_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2408_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2408,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[601,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2409","image_path":"images/combination3d_2409.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2409_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2409_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2409_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2409_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2409_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2409,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[3,0,0]],[[0,0,2],[0,1,1],[0,1,2],[0,2,2],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[562,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2410","image_path":"images/combination3d_2410.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2410_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2410_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2410_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2410_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2410_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2410,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":9}],"canvas_size":[563,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2411","image_path":"images/combination3d_2411.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2411_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2411_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2411_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2411_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2411_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2411,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[3,0,0],[3,1,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8}],"canvas_size":[593,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2412","image_path":"images/combination3d_2412.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2412_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2412_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2412_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2412_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2412_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2412,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[2,4,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,1],[2,2,2],[2,3,1],[2,3,2],[2,4,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,2,0]]],"total_cube_count":13}],"canvas_size":[605,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2413","image_path":"images/combination3d_2413.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2413_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2413_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2413_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2413_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2413_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2413,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[2,0,1]]],"total_cube_count":11}],"canvas_size":[570,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2414","image_path":"images/combination3d_2414.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2414_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2414_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2414_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,5","question_id":"combination3d_2414_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2414_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2414,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[618,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2415","image_path":"images/combination3d_2415.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2415_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2415_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2415_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2415_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2415_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2415,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[590,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2416","image_path":"images/combination3d_2416.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2416_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2416_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2416_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2416_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2416_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2416,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,2],[0,2,3],[1,0,3],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[614,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2417","image_path":"images/combination3d_2417.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2417_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2417_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2417_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2417_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2417_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2417,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[579,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2418","image_path":"images/combination3d_2418.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2418_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2418_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2418_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2418_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2418_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2418,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,4,0],[1,4,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,1,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,4,0],[3,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[2,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,3],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[555,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2419","image_path":"images/combination3d_2419.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2419_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2419_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2419_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2419_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2419_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2419,"target_cube_count":13,"target_cubes":[[0,1,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,5,0],[1,0,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,5,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[3,0,0],[4,0,0],[5,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,5,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[592,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2420","image_path":"images/combination3d_2420.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2420_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2420_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2420_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2420_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2420_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2420,"target_cube_count":12,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,5,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[552,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2421","image_path":"images/combination3d_2421.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2421_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2421_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2421_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2421_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2421_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2421,"target_cube_count":8,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[613,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2422","image_path":"images/combination3d_2422.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2422_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2422_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2422_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2422_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2422_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2422,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[578,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2423","image_path":"images/combination3d_2423.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2423_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2423_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2423_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_2423_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2423_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2423,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8}],"canvas_size":[587,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2424","image_path":"images/combination3d_2424.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2424_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2424_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2424_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2424_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2424_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2424,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,2,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[2,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[585,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2425","image_path":"images/combination3d_2425.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2425_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2425_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2425_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2425_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_2425_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2425,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[0,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[4,1,0],[4,1,1],[4,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[4,1,0],[4,1,1],[4,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,1],[1,2,1],[2,2,0],[2,2,1],[3,1,1],[3,2,0],[3,2,1],[4,0,1],[4,1,1],[4,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[618,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2426","image_path":"images/combination3d_2426.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2426_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2426_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2426_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2426_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2426_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2426,"target_cube_count":13,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[4,1,0],[4,1,1],[4,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":10}],"canvas_size":[602,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2427","image_path":"images/combination3d_2427.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2427_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2427_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2427_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2427_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2427_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2427,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,0],[0,3,1],[1,3,0],[1,3,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0],[3,1,1],[3,1,2],[3,1,3]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":13}],"canvas_size":[590,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2428","image_path":"images/combination3d_2428.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2428_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2428_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2428_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2428_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2428_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2428,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,2,2],[2,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[595,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2429","image_path":"images/combination3d_2429.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2429_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2429_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2429_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2429_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2429_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2429,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[564,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2430","image_path":"images/combination3d_2430.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2430_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2430_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2430_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2430_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2430_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2430,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[598,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2431","image_path":"images/combination3d_2431.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2431_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2431_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2431_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2431_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2431_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2431,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,2]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[593,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2432","image_path":"images/combination3d_2432.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2432_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2432_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2432_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2432_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2432_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2432,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,1],[1,0,2],[1,1,2],[2,0,1],[2,1,1],[2,2,1],[3,0,1],[4,0,0],[4,0,1],[4,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[0,4,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,2]]],"total_cube_count":15}],"canvas_size":[589,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2433","image_path":"images/combination3d_2433.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2433_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2433_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2433_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_2433_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2433_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2433,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[2,0,2],[2,1,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,1],[2,0,1],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[599,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2434","image_path":"images/combination3d_2434.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2434_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2434_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2434_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2434_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2434_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2434,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,3],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2],[1,2,3],[1,2,4]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[3,0,1],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15}],"canvas_size":[581,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2435","image_path":"images/combination3d_2435.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2435_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2435_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2435_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2435_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2435_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2435,"target_cube_count":14,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[2,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":11}],"canvas_size":[558,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2436","image_path":"images/combination3d_2436.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2436_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2436_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2436_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2436_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2436_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2436,"target_cube_count":11,"target_cubes":[[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,4,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,2],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":15}],"canvas_size":[614,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2437","image_path":"images/combination3d_2437.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2437_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2437_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2437_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2437_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_2437_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2437,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":9}],"canvas_size":[609,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2438","image_path":"images/combination3d_2438.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2438_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2438_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2438_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2438_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2438_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2438,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,1],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,1],[1,3,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":13}],"canvas_size":[553,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2439","image_path":"images/combination3d_2439.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2439_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2439_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2439_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2439_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2439_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2439,"target_cube_count":13,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,2,1],[2,3,0],[2,4,0],[2,4,1],[2,5,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[612,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2440","image_path":"images/combination3d_2440.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2440_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2440_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2440_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2440_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2440_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2440,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,2,0]],[[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[2,1,1],[2,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[598,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2441","image_path":"images/combination3d_2441.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2441_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2441_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2441_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2441_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2441_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2441,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[4,0,0],[4,0,1],[4,1,0],[4,1,1],[5,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[593,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2442","image_path":"images/combination3d_2442.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2442_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2442_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2442_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2442_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2442_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2442,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,2],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,1],[2,0,2],[2,1,1],[3,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3],[2,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3],[2,0,2]]],"total_cube_count":13}],"canvas_size":[605,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2443","image_path":"images/combination3d_2443.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2443_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2443_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2443_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2443_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2443_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2443,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,2],[0,4,0],[1,1,1],[1,2,1],[1,4,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[608,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2444","image_path":"images/combination3d_2444.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2444_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2444_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2444_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2444_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2444_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2444,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,0,1],[1,2,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":13}],"canvas_size":[608,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2445","image_path":"images/combination3d_2445.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2445_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2445_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2445_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2445_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2445_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2445,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[597,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2446","image_path":"images/combination3d_2446.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2446_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2446_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2446_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2446_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2446_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2446,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,3,1],[1,1,1],[1,2,1],[1,3,1],[2,0,1],[2,0,2],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,0]]],"total_cube_count":14}],"canvas_size":[605,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2447","image_path":"images/combination3d_2447.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2447_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2447_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2447_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2447_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2447_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2447,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[610,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2448","image_path":"images/combination3d_2448.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2448_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2448_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2448_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2448_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2448_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2448,"target_cube_count":8,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,0,1]]],"total_cube_count":13}],"canvas_size":[560,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2449","image_path":"images/combination3d_2449.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2449_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2449_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2449_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_2449_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2449_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2449,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,2,2],[0,3,1],[0,3,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,2],[2,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,2],[1,2,0],[1,2,2],[2,0,2],[2,1,2],[2,2,2],[2,2,3]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[612,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2450","image_path":"images/combination3d_2450.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2450_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2450_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2450_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2450_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2450_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2450,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,3],[0,1,4],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,2]]],"total_cube_count":14}],"canvas_size":[581,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2451","image_path":"images/combination3d_2451.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2451_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2451_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2451_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2451_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2451_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2451,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,1],[1,0,2],[1,1,2],[1,1,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":13}],"canvas_size":[574,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2452","image_path":"images/combination3d_2452.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2452_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2452_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2452_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2452_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2452_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2452,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,2,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":9}],"canvas_size":[611,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2453","image_path":"images/combination3d_2453.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2453_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2453_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2453_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2453_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2453_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2453,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1]]],"total_cube_count":12}],"canvas_size":[577,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2454","image_path":"images/combination3d_2454.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2454_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2454_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2454_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2454_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2454_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2454,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,3,2],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,2],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[3,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13}],"canvas_size":[611,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2455","image_path":"images/combination3d_2455.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2455_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2455_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2455_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2455_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2455_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2455,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":10}],"canvas_size":[556,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2456","image_path":"images/combination3d_2456.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2456_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2456_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2456_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2456_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2456_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2456,"target_cube_count":10,"target_cubes":[[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[2,0,1]],[[0,1,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":14}],"canvas_size":[555,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2457","image_path":"images/combination3d_2457.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2457_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2457_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2457_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2457_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2457_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2457,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,0,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[573,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2458","image_path":"images/combination3d_2458.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2458_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2458_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2458_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2458_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2458_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2458,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,2],[0,2,3],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,1,2],[2,2,2],[2,2,3]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[594,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2459","image_path":"images/combination3d_2459.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2459_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2459_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2459_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2459_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2459_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2459,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,1,0],[3,1,1],[4,0,0],[4,1,0],[4,1,1],[5,1,0],[6,1,0],[6,2,0],[6,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[559,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2460","image_path":"images/combination3d_2460.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2460_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2460_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2460_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2460_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2460_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2460,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,0,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,3],[1,0,1],[1,0,2],[1,0,3],[1,1,3]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[2,3,0]]],"total_cube_count":13}],"canvas_size":[555,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2461","image_path":"images/combination3d_2461.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2461_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2461_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2461_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2461_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2461_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2461,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,1,1],[3,0,1],[3,1,0],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,1,1],[3,0,1],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10}],"canvas_size":[566,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2462","image_path":"images/combination3d_2462.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2462_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2462_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2462_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2462_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2462_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2462,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[564,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2463","image_path":"images/combination3d_2463.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2463_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2463_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2463_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2463_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2463_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2463,"target_cube_count":9,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[1,2,2],[1,3,1],[2,1,1],[2,2,1],[2,3,1],[2,3,2],[2,4,0],[2,4,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,0],[1,0,1],[1,2,1],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,4,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[613,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2464","image_path":"images/combination3d_2464.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2464_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2464_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2464_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2464_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_2464_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2464,"target_cube_count":14,"target_cubes":[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8}],"canvas_size":[616,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2465","image_path":"images/combination3d_2465.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2465_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2465_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2465_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2465_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2465_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2465,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,3],[2,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[593,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2466","image_path":"images/combination3d_2466.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2466_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2466_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2466_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2466_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_2466_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2466,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[574,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2467","image_path":"images/combination3d_2467.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2467_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2467_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2467_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2467_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2467_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2467,"target_cube_count":8,"target_cubes":[[0,3,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,2],[0,2,3],[1,0,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,2,0],[1,2,1],[1,3,0],[2,3,0],[2,4,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[585,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2468","image_path":"images/combination3d_2468.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2468_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2468_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2468_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2468_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2468_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2468,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1],[2,2,2],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[582,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2469","image_path":"images/combination3d_2469.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2469_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2469_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2469_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2469_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2469_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2469,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2],[0,2,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2],[0,2,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[1,4,1],[2,1,1],[2,3,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]]],"total_cube_count":14}],"canvas_size":[583,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2470","image_path":"images/combination3d_2470.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2470_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2470_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2470_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2470_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2470_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2470,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,1,0],[0,1,1],[1,0,2],[1,1,1],[1,1,2],[2,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[602,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2471","image_path":"images/combination3d_2471.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2471_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2471_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2471_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2471_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2471_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2471,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":13}],"canvas_size":[600,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2472","image_path":"images/combination3d_2472.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2472_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2472_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2472_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2472_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2472_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2472,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,3],[0,0,4],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10}],"canvas_size":[596,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2473","image_path":"images/combination3d_2473.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2473_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2473_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2473_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_2473_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2473_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2473,"target_cube_count":10,"target_cubes":[[0,2,0],[1,2,0],[2,2,0],[2,3,0],[2,4,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[2,1,0],[2,1,1],[2,2,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[605,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2474","image_path":"images/combination3d_2474.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2474_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2474_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2474_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2474_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2474_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2474,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,2],[2,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,2,0],[2,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,2,0],[3,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[554,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2475","image_path":"images/combination3d_2475.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2475_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2475_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2475_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2475_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2475_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2475,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[574,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2476","image_path":"images/combination3d_2476.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2476_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2476_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2476_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2476_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2476_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2476,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,3],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,1]]],"total_cube_count":11}],"canvas_size":[579,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2477","image_path":"images/combination3d_2477.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2477_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2477_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2477_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2477_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2477_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2477,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1],[2,1,1],[3,0,1],[3,0,2],[3,0,3],[3,1,1],[3,1,2],[4,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,1,5]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,1],[0,4,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[1,4,0],[1,4,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[574,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2478","image_path":"images/combination3d_2478.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2478_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2478_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2478_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2478_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2478_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2478,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2]],[[0,1,1],[1,0,1],[1,1,1],[2,0,1],[3,0,0],[3,0,1],[4,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[601,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2479","image_path":"images/combination3d_2479.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2479_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2479_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2479_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2479_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2479_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2479,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,1,1],[2,1,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0]]],"total_cube_count":12}],"canvas_size":[560,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2480","image_path":"images/combination3d_2480.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2480_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2480_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2480_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2480_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2480_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2480,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[1,0,1],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[564,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2481","image_path":"images/combination3d_2481.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2481_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2481_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2481_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2481_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2481_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2481,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[0,1,2],[0,1,3],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,0,2],[2,0,3],[2,1,1],[2,2,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,2],[2,1,2],[2,2,1],[2,2,2]]],"total_cube_count":14}],"canvas_size":[575,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2482","image_path":"images/combination3d_2482.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2482_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2482_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2482_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2482_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2482_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2482,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,0],[4,1,0],[4,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[4,1,0],[4,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,3],[1,1,0],[1,1,3],[1,1,4],[2,0,3]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[618,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2483","image_path":"images/combination3d_2483.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2483_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2483_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2483_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2483_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2483_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2483,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,2],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[581,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2484","image_path":"images/combination3d_2484.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2484_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2484_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2484_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_2484_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2484_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2484,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2],[3,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,2,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,2],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,1,3],[1,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1],[1,2,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,2,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[2,3,1]]],"total_cube_count":15}],"canvas_size":[550,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2485","image_path":"images/combination3d_2485.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2485_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2485_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2485_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2485_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2485_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2485,"target_cube_count":14,"target_cubes":[[0,2,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[3,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[614,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2486","image_path":"images/combination3d_2486.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2486_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2486_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2486_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2486_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2486_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2486,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[4,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,4,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2]]],"total_cube_count":14}],"canvas_size":[583,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2487","image_path":"images/combination3d_2487.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2487_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2487_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2487_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2487_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2487_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2487,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[0,4,0],[0,4,1],[0,4,2],[0,4,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[2,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":9}],"canvas_size":[594,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2488","image_path":"images/combination3d_2488.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2488_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2488_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2488_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2488_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2488_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2488,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[570,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2489","image_path":"images/combination3d_2489.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2489_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2489_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2489_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2489_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2489_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2489,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,3,0],[0,4,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[2,3,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":13}],"canvas_size":[587,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2490","image_path":"images/combination3d_2490.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2490_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2490_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2490_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2490_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2490_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2490,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,1,1],[3,2,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,0],[1,1,2],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,2,0],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,1,1],[1,1,2],[1,2,1],[2,0,2],[2,1,2]],[[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":13}],"canvas_size":[572,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2491","image_path":"images/combination3d_2491.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2491_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2491_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2491_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_2491_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2491_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2491,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,0],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[606,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2492","image_path":"images/combination3d_2492.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2492_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2492_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2492_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2492_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2492_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2492,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]]],"total_cube_count":9}],"canvas_size":[571,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2493","image_path":"images/combination3d_2493.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2493_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2493_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2493_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2493_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2493_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2493,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,2,1],[3,1,1],[3,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[573,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2494","image_path":"images/combination3d_2494.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2494_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2494_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2494_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2494_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2494_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2494,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,0],[0,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":13}],"canvas_size":[561,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2495","image_path":"images/combination3d_2495.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2495_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2495_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2495_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2495_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2495_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2495,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[2,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,1,0],[2,2,0]]],"total_cube_count":10}],"canvas_size":[562,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2496","image_path":"images/combination3d_2496.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2496_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2496_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2496_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2496_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2496_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2496,"target_cube_count":10,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0]]],"total_cube_count":10}],"canvas_size":[607,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2497","image_path":"images/combination3d_2497.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2497_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2497_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2497_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2497_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2497_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2497,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[573,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2498","image_path":"images/combination3d_2498.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2498_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2498_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2498_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2498_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2498_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2498,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,2,0],[2,2,1],[2,2,2],[3,0,0],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[583,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2499","image_path":"images/combination3d_2499.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2499_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2499_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2499_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2499_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2499_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2499,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[3,0,1],[3,1,1],[3,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1],[4,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[551,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2500","image_path":"images/combination3d_2500.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2500_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2500_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2500_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2500_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2500_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2500,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,0,2],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9}],"canvas_size":[572,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2501","image_path":"images/combination3d_2501.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2501_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2501_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2501_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2501_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,5","question_id":"combination3d_2501_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2501,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[568,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2502","image_path":"images/combination3d_2502.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2502_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2502_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2502_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2502_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2502_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2502,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,0],[0,3,1],[0,3,2],[0,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[4,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0]]],"total_cube_count":11}],"canvas_size":[590,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2503","image_path":"images/combination3d_2503.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2503_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2503_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2503_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2503_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_2503_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2503,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3],[3,0,4],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14}],"canvas_size":[565,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2504","image_path":"images/combination3d_2504.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2504_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2504_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2504_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_2504_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2504_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2504,"target_cube_count":14,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[588,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2505","image_path":"images/combination3d_2505.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2505_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2505_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2505_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2505_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_2505_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2505,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,2],[1,1,2],[2,0,2],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,0,2],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[606,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2506","image_path":"images/combination3d_2506.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2506_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2506_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2506_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2506_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2506_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2506,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]],[[0,2,1],[0,3,1],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[2,1,2],[2,2,0],[2,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13}],"canvas_size":[564,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2507","image_path":"images/combination3d_2507.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2507_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2507_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2507_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2507_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2507_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2507,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[568,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2508","image_path":"images/combination3d_2508.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2508_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2508_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2508_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2508_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2508_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2508,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8}],"canvas_size":[613,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2509","image_path":"images/combination3d_2509.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2509_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2509_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2509_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2509_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2509_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2509,"target_cube_count":8,"target_cubes":[[0,2,0],[0,3,0],[1,2,0],[2,2,0],[3,2,0],[4,0,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[614,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2510","image_path":"images/combination3d_2510.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2510_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2510_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2510_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2510_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2510_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2510,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,3,1],[2,0,2],[2,1,0],[2,1,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[601,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2511","image_path":"images/combination3d_2511.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2511_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2511_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2511_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_2511_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2511_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2511,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[565,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2512","image_path":"images/combination3d_2512.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2512_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2512_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2512_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2512_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2512_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2512,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,1],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,2],[1,0,2],[1,1,0],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,3],[0,2,2],[0,2,3],[0,3,2],[0,4,0],[0,4,1],[0,4,2],[0,4,3],[1,1,3]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]]],"total_cube_count":14}],"canvas_size":[597,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2513","image_path":"images/combination3d_2513.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2513_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2513_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2513_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2513_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2513_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2513,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]]],"total_cube_count":12}],"canvas_size":[562,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2514","image_path":"images/combination3d_2514.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2514_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2514_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2514_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2514_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2514_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2514,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[2,3,2],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,1],[1,0,2],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,4],[1,3,2],[1,3,3],[1,3,4],[2,2,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1]]],"total_cube_count":14}],"canvas_size":[577,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2515","image_path":"images/combination3d_2515.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2515_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2515_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2515_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2515_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2515_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2515,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,3,0],[2,3,1],[2,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,2],[2,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[591,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2516","image_path":"images/combination3d_2516.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2516_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2516_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2516_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2516_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2516_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2516,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2]],[[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2]],[[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,3],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,1,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3]],[[0,0,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]]],"total_cube_count":14}],"canvas_size":[576,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2517","image_path":"images/combination3d_2517.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2517_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2517_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2517_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2517_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2517_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2517,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[0,5,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,5,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[2,1,1],[2,1,2],[3,0,2],[3,1,2],[3,1,3]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[603,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2518","image_path":"images/combination3d_2518.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2518_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2518_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2518_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2518_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2518_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2518,"target_cube_count":11,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[4,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[3,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,0,2],[4,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[552,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2519","image_path":"images/combination3d_2519.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2519_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2519_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2519_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2519_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2519_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2519,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[619,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2520","image_path":"images/combination3d_2520.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2520_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2520_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2520_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2520_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2520_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2520,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,1,0],[1,1,1],[1,1,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2],[2,1,2],[3,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,1,4],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,0],[2,1,0],[2,1,1],[2,1,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[3,0,1],[3,1,1],[4,0,1]]],"total_cube_count":13}],"canvas_size":[582,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2521","image_path":"images/combination3d_2521.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2521_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2521_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2521_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2521_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2521_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2521,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[593,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2522","image_path":"images/combination3d_2522.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2522_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2522_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2522_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2522_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2522_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2522,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1],[3,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,2],[1,1,3],[1,1,4],[1,1,5]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[2,1,1],[2,1,2],[3,0,2],[3,1,1],[3,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[563,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2523","image_path":"images/combination3d_2523.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2523_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2523_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2523_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2523_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_2523_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2523,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[0,2,0],[0,3,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[559,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2524","image_path":"images/combination3d_2524.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2524_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2524_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2524_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2524_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2524_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2524,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9}],"canvas_size":[587,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2525","image_path":"images/combination3d_2525.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2525_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2525_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2525_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_2525_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2525_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2525,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[4,1,0],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,2,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,2,2],[1,0,3]]],"total_cube_count":12}],"canvas_size":[578,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2526","image_path":"images/combination3d_2526.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2526_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2526_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2526_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2526_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2526_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2526,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":10}],"canvas_size":[567,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2527","image_path":"images/combination3d_2527.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2527_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2527_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2527_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2527_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2527_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2527,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[585,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2528","image_path":"images/combination3d_2528.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2528_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2528_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2528_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2528_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2528_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2528,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,3],[1,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,1],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[1,4,1],[1,4,2]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12}],"canvas_size":[584,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2529","image_path":"images/combination3d_2529.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2529_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2529_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2529_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,5","question_id":"combination3d_2529_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2529_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2529,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,2,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,2]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,3],[1,0,0],[1,0,1],[1,1,1],[1,1,3],[1,2,1],[1,2,2],[1,2,3],[2,1,1],[2,2,1],[2,2,3]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14}],"canvas_size":[614,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2530","image_path":"images/combination3d_2530.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2530_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2530_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2530_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2530_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2530_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2530,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,1],[0,1,2],[1,1,1],[2,1,1],[3,1,1],[4,0,0],[4,0,1],[4,1,1],[4,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[0,4,0],[0,4,1],[1,0,1],[1,4,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[0,1,1],[1,1,0],[2,1,0],[3,1,0],[4,0,0],[4,1,0],[4,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[607,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2531","image_path":"images/combination3d_2531.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2531_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2531_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2531_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2531_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2531_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2531,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1],[4,0,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8}],"canvas_size":[580,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2532","image_path":"images/combination3d_2532.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2532_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2532_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2532_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2532_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2532_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2532,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1],[2,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[2,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":11}],"canvas_size":[557,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2533","image_path":"images/combination3d_2533.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2533_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2533_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2533_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2533_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2533_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2533,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[3,2,1],[3,2,2],[3,3,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,3,0]],[[0,1,0],[0,1,1],[1,1,1],[2,1,1],[3,0,1],[3,1,1],[3,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1],[3,2,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1],[3,2,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[0,2,1],[0,2,2],[0,3,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,2,1]]],"total_cube_count":14}],"canvas_size":[618,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2534","image_path":"images/combination3d_2534.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2534_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2534_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2534_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2534_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2534_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2534,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[555,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2535","image_path":"images/combination3d_2535.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2535_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2535_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2535_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2535_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2535_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2535,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,2,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[603,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2536","image_path":"images/combination3d_2536.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2536_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2536_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2536_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2536_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2536_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2536,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":9}],"canvas_size":[555,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2537","image_path":"images/combination3d_2537.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2537_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2537_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2537_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2537_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2537_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2537,"target_cube_count":9,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[611,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2538","image_path":"images/combination3d_2538.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2538_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2538_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2538_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2538_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2538_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2538,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[603,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2539","image_path":"images/combination3d_2539.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2539_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2539_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2539_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2539_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2539_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2539,"target_cube_count":8,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,1,0],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[555,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2540","image_path":"images/combination3d_2540.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2540_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2540_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2540_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2540_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2540_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2540,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[618,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2541","image_path":"images/combination3d_2541.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2541_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2541_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2541_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2541_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2541_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2541,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,2,1],[1,1,2],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,1,2],[2,2,0],[2,2,1],[2,2,2]]],"total_cube_count":13}],"canvas_size":[558,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2542","image_path":"images/combination3d_2542.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2542_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2542_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2542_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_2542_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2542_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2542,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8}],"canvas_size":[551,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2543","image_path":"images/combination3d_2543.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2543_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2543_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2543_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2543_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2543_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2543,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,1,1],[2,2,0],[2,2,1],[3,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,4,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,1,2],[2,0,1],[2,0,2],[3,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1]]],"total_cube_count":13}],"canvas_size":[620,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2544","image_path":"images/combination3d_2544.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2544_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2544_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2544_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2544_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2544_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2544,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,2,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[609,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2545","image_path":"images/combination3d_2545.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2545_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2545_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2545_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2545_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2545_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2545,"target_cube_count":12,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[592,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2546","image_path":"images/combination3d_2546.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2546_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2546_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2546_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2546_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_2546_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2546,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[0,3,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,2,0],[0,2,1],[0,3,1],[1,2,0],[1,2,1],[1,3,1],[2,0,1],[2,1,1],[2,1,2],[2,2,1],[3,2,1]]],"total_cube_count":14}],"canvas_size":[591,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2547","image_path":"images/combination3d_2547.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2547_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2547_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2547_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2547_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2547_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2547,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[584,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2548","image_path":"images/combination3d_2548.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2548_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2548_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2548_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2548_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2548_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2548,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8}],"canvas_size":[572,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2549","image_path":"images/combination3d_2549.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2549_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2549_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2549_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2549_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2549_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2549,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,0,1],[4,0,0],[4,0,1],[4,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,0,1],[4,0,0],[4,0,1],[4,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,2,0],[1,2,0],[2,2,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0],[4,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[573,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2550","image_path":"images/combination3d_2550.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2550_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2550_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2550_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2550_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2550_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2550,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[4,1,0],[4,1,1],[4,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,2],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0],[4,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]]],"total_cube_count":12}],"canvas_size":[570,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2551","image_path":"images/combination3d_2551.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2551_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2551_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2551_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,5","question_id":"combination3d_2551_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2551_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2551,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,2,0],[1,1,0],[1,2,0],[2,0,1],[2,1,1],[2,2,0],[2,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,1],[1,0,1],[1,0,2],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":12}],"canvas_size":[556,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2552","image_path":"images/combination3d_2552.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2552_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2552_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2552_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2552_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2552_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2552,"target_cube_count":12,"target_cubes":[[0,3,0],[1,1,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[2,4,1],[2,4,2],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,2]],[[0,1,0],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[2,1,0],[3,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0]]],"total_cube_count":14}],"canvas_size":[567,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2553","image_path":"images/combination3d_2553.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2553_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2553_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2553_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2553_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2553_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2553,"target_cube_count":14,"target_cubes":[[0,2,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,0,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,2],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,1],[2,2,2],[3,0,1],[3,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[591,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2554","image_path":"images/combination3d_2554.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2554_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2554_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2554_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2554_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2554_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2554,"target_cube_count":13,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,2]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[0,1,4],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[589,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2555","image_path":"images/combination3d_2555.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2555_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2555_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2555_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_2555_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2555_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2555,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[563,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2556","image_path":"images/combination3d_2556.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2556_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2556_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2556_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_2556_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2556_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2556,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,3,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[550,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2557","image_path":"images/combination3d_2557.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2557_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2557_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2557_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2557_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2557_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2557,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10}],"canvas_size":[614,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2558","image_path":"images/combination3d_2558.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2558_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2558_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2558_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2558_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2558_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2558,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]],[[0,0,2],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,1,1],[3,0,0],[3,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]]],"total_cube_count":14}],"canvas_size":[589,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2559","image_path":"images/combination3d_2559.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2559_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2559_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2559_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2559_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2559_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2559,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[607,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2560","image_path":"images/combination3d_2560.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2560_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2560_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2560_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2560_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2560_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2560,"target_cube_count":10,"target_cubes":[[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,0,2],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11}],"canvas_size":[568,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2561","image_path":"images/combination3d_2561.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2561_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2561_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2561_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2561_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2561_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2561,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[1,0,2],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":11}],"canvas_size":[589,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2562","image_path":"images/combination3d_2562.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2562_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2562_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2562_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2562_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2562_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2562,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,1,1],[4,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12}],"canvas_size":[620,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2563","image_path":"images/combination3d_2563.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2563_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2563_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2563_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_2563_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2563_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2563,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12}],"canvas_size":[562,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2564","image_path":"images/combination3d_2564.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2564_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2564_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2564_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_2564_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2564_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2564,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[563,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2565","image_path":"images/combination3d_2565.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2565_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2565_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2565_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2565_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2565_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2565,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[1,1,0],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[563,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2566","image_path":"images/combination3d_2566.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2566_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2566_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2566_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2566_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2566_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2566,"target_cube_count":9,"target_cubes":[[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,3],[0,1,2],[1,0,1],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[3,0,0],[3,0,1]]],"total_cube_count":14}],"canvas_size":[595,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2567","image_path":"images/combination3d_2567.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2567_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2567_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2567_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_2567_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2567_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2567,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[1,1,3],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[612,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2568","image_path":"images/combination3d_2568.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2568_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2568_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2568_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2568_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2568_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2568,"target_cube_count":12,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,2],[0,1,0],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15}],"canvas_size":[614,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2569","image_path":"images/combination3d_2569.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2569_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2569_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2569_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2569_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_2569_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2569,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,3],[3,0,0],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,1],[2,0,2],[2,0,4],[3,0,0],[3,0,1],[3,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,1,1],[1,1,1],[1,1,2],[1,1,3],[1,2,3],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0]]],"total_cube_count":13}],"canvas_size":[552,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2570","image_path":"images/combination3d_2570.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2570_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2570_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2570_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2570_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2570_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2570,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":9}],"canvas_size":[569,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2571","image_path":"images/combination3d_2571.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2571_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2571_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2571_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2571_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2571_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2571,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[556,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2572","image_path":"images/combination3d_2572.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2572_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2572_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2572_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2572_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2572_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2572,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,3],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11}],"canvas_size":[564,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2573","image_path":"images/combination3d_2573.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2573_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2573_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2573_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2573_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2573_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2573,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9}],"canvas_size":[554,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2574","image_path":"images/combination3d_2574.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2574_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2574_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2574_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2574_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2574_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2574,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[589,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2575","image_path":"images/combination3d_2575.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2575_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2575_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2575_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2575_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2575_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2575,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[1,0,1],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[1,0,1],[1,1,1]]],"total_cube_count":8}],"canvas_size":[599,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2576","image_path":"images/combination3d_2576.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2576_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2576_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2576_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2576_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2576_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2576,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[596,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2577","image_path":"images/combination3d_2577.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2577_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2577_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2577_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2577_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2577_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2577,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,2],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,2,0],[2,2,1],[2,3,1],[2,3,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":15}],"canvas_size":[606,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2578","image_path":"images/combination3d_2578.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2578_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2578_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2578_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2578_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2578_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2578,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,1,1],[0,1,2],[0,2,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":10}],"canvas_size":[596,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2579","image_path":"images/combination3d_2579.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2579_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2579_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2579_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2579_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2579_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2579,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[562,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2580","image_path":"images/combination3d_2580.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2580_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2580_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2580_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2580_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2580_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2580,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1],[2,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9}],"canvas_size":[567,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2581","image_path":"images/combination3d_2581.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2581_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2581_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2581_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2581_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2581_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2581,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[567,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2582","image_path":"images/combination3d_2582.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2582_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2582_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2582_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2582_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2582_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2582,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,3,1],[1,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,1,1],[1,2,1],[1,3,1],[1,3,2],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[592,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2583","image_path":"images/combination3d_2583.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2583_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2583_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2583_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2583_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2583_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2583,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]]],"total_cube_count":13}],"canvas_size":[588,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2584","image_path":"images/combination3d_2584.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2584_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2584_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2584_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2584_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2584_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2584,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[0,2,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1]]],"total_cube_count":9}],"canvas_size":[563,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2585","image_path":"images/combination3d_2585.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2585_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2585_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2585_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2585_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2585_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2585,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[587,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2586","image_path":"images/combination3d_2586.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2586_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2586_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2586_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2586_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2586_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2586,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[582,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2587","image_path":"images/combination3d_2587.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2587_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2587_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2587_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2587_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2587_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2587,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[0,4,0],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[1,4,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12}],"canvas_size":[566,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2588","image_path":"images/combination3d_2588.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2588_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2588_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2588_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2588_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_2588_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2588,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,1,1],[3,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,2,0],[1,2,1],[1,2,2],[2,2,1],[2,2,2],[3,0,1],[3,1,1],[3,1,2],[3,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[1,1,2],[1,2,2],[1,3,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":13}],"canvas_size":[563,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2589","image_path":"images/combination3d_2589.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2589_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2589_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2589_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2589_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2589_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2589,"target_cube_count":13,"target_cubes":[[0,2,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3],[3,1,0],[3,1,1],[3,1,2],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[2,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[564,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2590","image_path":"images/combination3d_2590.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2590_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2590_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2590_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2590_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2590_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2590,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[594,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2591","image_path":"images/combination3d_2591.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2591_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2591_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2591_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2591_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2591_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2591,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,1,0],[1,2,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":9}],"canvas_size":[620,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2592","image_path":"images/combination3d_2592.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2592_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2592_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2592_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_2592_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2592_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2592,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]],[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]],[[0,0,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,0,2],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,2]]],"total_cube_count":11}],"canvas_size":[608,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2593","image_path":"images/combination3d_2593.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2593_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2593_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2593_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2593_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2593_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2593,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,0],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[591,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2594","image_path":"images/combination3d_2594.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2594_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2594_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2594_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2594_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2594_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2594,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3],[2,0,2],[2,0,3],[3,0,2],[4,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[2,3,0],[3,2,0],[4,2,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[3,2,0],[4,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,2],[1,0,1]]],"total_cube_count":14}],"canvas_size":[581,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2595","image_path":"images/combination3d_2595.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2595_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2595_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2595_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2595_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2595_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2595,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[2,2,0],[2,2,1],[2,3,0],[3,2,0],[3,2,1],[3,2,2],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,2],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,1,0],[1,2,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":8}],"canvas_size":[568,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2596","image_path":"images/combination3d_2596.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2596_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2596_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2596_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_2596_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2596_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2596,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,3],[0,1,2],[0,1,3],[0,2,3],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12}],"canvas_size":[618,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2597","image_path":"images/combination3d_2597.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2597_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2597_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2597_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2597_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2597_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2597,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[600,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2598","image_path":"images/combination3d_2598.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2598_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2598_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2598_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2598_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2598_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2598,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,1,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1],[3,0,1],[3,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[614,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2599","image_path":"images/combination3d_2599.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2599_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2599_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2599_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2599_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_2599_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2599,"target_cube_count":10,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[614,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2600","image_path":"images/combination3d_2600.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2600_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2600_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2600_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2600_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2600_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2600,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[3,0,0],[3,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,2,0],[0,3,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,1],[1,4,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,3,1],[0,4,1],[1,4,0],[1,4,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[3,3,0],[3,4,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[3,0,0],[3,0,1],[3,1,0]]],"total_cube_count":14}],"canvas_size":[550,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2601","image_path":"images/combination3d_2601.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2601_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2601_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2601_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2601_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2601_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2601,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,0,4],[2,1,0],[2,1,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[2,0,2],[2,1,1]]],"total_cube_count":10}],"canvas_size":[561,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2602","image_path":"images/combination3d_2602.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2602_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2602_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2602_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2602_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2602_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2602,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,2],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,2,1],[2,2,1],[2,2,2],[3,2,0],[3,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10}],"canvas_size":[588,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2603","image_path":"images/combination3d_2603.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2603_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2603_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2603_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2603_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2603_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2603,"target_cube_count":10,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[550,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2604","image_path":"images/combination3d_2604.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2604_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2604_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2604_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2604_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2604_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2604,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[617,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2605","image_path":"images/combination3d_2605.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2605_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2605_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2605_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2605_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2605_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2605,"target_cube_count":10,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,2,0],[3,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,1,0]]],"total_cube_count":9}],"canvas_size":[603,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2606","image_path":"images/combination3d_2606.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2606_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2606_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2606_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2606_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2606_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2606,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[575,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2607","image_path":"images/combination3d_2607.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2607_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2607_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2607_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2607_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_2607_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2607,"target_cube_count":12,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,2,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,2,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1],[2,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":13}],"canvas_size":[582,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2608","image_path":"images/combination3d_2608.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2608_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2608_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2608_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2608_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2608_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2608,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1]],[[0,1,1],[1,0,2],[1,0,3],[1,1,1],[1,1,2],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0],[3,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13}],"canvas_size":[555,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2609","image_path":"images/combination3d_2609.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2609_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2609_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2609_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2609_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2609_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2609,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[613,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2610","image_path":"images/combination3d_2610.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2610_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2610_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2610_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2610_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2610_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2610,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,2,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,2],[1,0,1],[1,2,2],[2,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,1,1],[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[2,0,0],[2,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,2,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":13}],"canvas_size":[603,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2611","image_path":"images/combination3d_2611.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2611_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2611_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2611_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2611_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2611_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2611,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[3,1,0],[4,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[572,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2612","image_path":"images/combination3d_2612.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2612_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2612_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2612_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2612_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2612_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2612,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[585,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2613","image_path":"images/combination3d_2613.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2613_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2613_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2613_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2613_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2613_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2613,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":10}],"canvas_size":[567,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2614","image_path":"images/combination3d_2614.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2614_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2614_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2614_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2614_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2614_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2614,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[589,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2615","image_path":"images/combination3d_2615.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2615_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2615_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2615_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_2615_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2615_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2615,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,1],[1,1,1],[1,2,1],[1,3,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1],[2,3,2]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,2,0],[2,2,1],[3,0,1],[3,1,1],[3,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,2],[1,2,3],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[609,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2616","image_path":"images/combination3d_2616.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2616_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2616_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2616_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2616_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2616_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2616,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[559,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2617","image_path":"images/combination3d_2617.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2617_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2617_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2617_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2617_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2617_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2617,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[3,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,2,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,0,2],[2,1,1],[2,2,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":15}],"canvas_size":[610,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2618","image_path":"images/combination3d_2618.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2618_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2618_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2618_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2618_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2618_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2618,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,3]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[620,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2619","image_path":"images/combination3d_2619.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2619_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2619_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2619_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2619_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2619_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2619,"target_cube_count":11,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[0,2,3],[1,0,0],[1,0,1],[1,0,2],[1,1,3],[2,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,2],[2,0,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[612,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2620","image_path":"images/combination3d_2620.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2620_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2620_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2620_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2620_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2620_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2620,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,1,1]]],"total_cube_count":15}],"canvas_size":[601,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2621","image_path":"images/combination3d_2621.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2621_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2621_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2621_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2621_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2621_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2621,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":8}],"canvas_size":[582,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2622","image_path":"images/combination3d_2622.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2622_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2622_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2622_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2622_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2622_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2622,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,1]]],"total_cube_count":11}],"canvas_size":[553,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2623","image_path":"images/combination3d_2623.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2623_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2623_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2623_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2623_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2623_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2623,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,3,0],[2,3,1],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[565,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2624","image_path":"images/combination3d_2624.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2624_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2624_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2624_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2624_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2624_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2624,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1]]],"total_cube_count":9}],"canvas_size":[560,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2625","image_path":"images/combination3d_2625.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2625_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2625_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2625_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2625_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,6","question_id":"combination3d_2625_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2625,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,1,1]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1]]],"total_cube_count":10}],"canvas_size":[587,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2626","image_path":"images/combination3d_2626.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2626_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2626_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2626_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2626_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2626_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2626,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[609,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2627","image_path":"images/combination3d_2627.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2627_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2627_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2627_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2627_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2627_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2627,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,1],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[587,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2628","image_path":"images/combination3d_2628.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2628_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2628_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2628_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2628_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2628_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2628,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[599,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2629","image_path":"images/combination3d_2629.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2629_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2629_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2629_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2629_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2629_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2629,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[1,0,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[1,0,1],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,2],[1,0,1],[1,1,1],[1,1,3]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[578,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2630","image_path":"images/combination3d_2630.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2630_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2630_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2630_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2630_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2630_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2630,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[582,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2631","image_path":"images/combination3d_2631.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2631_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2631_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2631_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2631_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2631_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2631,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,2,1],[1,3,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,2,1],[1,3,1],[1,3,2],[2,2,1],[2,3,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,1,2],[2,1,3],[3,1,2],[3,2,2],[3,2,3]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[3,1,1],[3,2,1],[3,2,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[581,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2632","image_path":"images/combination3d_2632.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2632_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2632_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2632_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2632_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2632_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2632,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1],[3,2,0],[3,2,1],[3,2,2],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,1],[1,1,2],[1,2,2]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,2,1],[1,2,2],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":12}],"canvas_size":[615,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2633","image_path":"images/combination3d_2633.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2633_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2633_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2633_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2633_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_2633_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2633,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2]],[[0,0,0],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,0],[0,3,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0],[3,3,0],[3,3,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[2,0,0]]],"total_cube_count":14}],"canvas_size":[601,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2634","image_path":"images/combination3d_2634.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2634_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2634_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2634_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_2634_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2634_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2634,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[1,3,3],[1,4,0],[1,4,1],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,0],[2,0,1],[2,1,2],[3,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,5,0],[1,2,0]]],"total_cube_count":14}],"canvas_size":[577,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2635","image_path":"images/combination3d_2635.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2635_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2635_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2635_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2635_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2635_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2635,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[604,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2636","image_path":"images/combination3d_2636.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2636_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2636_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2636_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2636_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2636_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2636,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],[[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,1]]],"total_cube_count":14}],"canvas_size":[582,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2637","image_path":"images/combination3d_2637.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2637_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2637_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2637_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2637_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2637_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2637,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[2,3,1],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[615,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2638","image_path":"images/combination3d_2638.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2638_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2638_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2638_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2638_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2638_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2638,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[2,1,0]],[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,1],[1,2,2],[1,2,3],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[585,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2639","image_path":"images/combination3d_2639.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2639_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2639_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2639_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2639_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2639_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2639,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[607,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2640","image_path":"images/combination3d_2640.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2640_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2640_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2640_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2640_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2640_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2640,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,2],[1,1,2]],[[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,2]]],"total_cube_count":14}],"canvas_size":[577,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2641","image_path":"images/combination3d_2641.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2641_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2641_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2641_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2641_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2641_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2641,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,2,3],[2,0,1],[2,1,1],[2,2,1],[2,3,1]]],"total_cube_count":14}],"canvas_size":[572,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2642","image_path":"images/combination3d_2642.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2642_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2642_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2642_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2642_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2642_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2642,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,2,2],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[575,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2643","image_path":"images/combination3d_2643.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2643_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2643_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2643_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,4","question_id":"combination3d_2643_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2643_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2643,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,1],[0,2,2],[1,2,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[1,4,1],[2,1,1],[2,1,2],[2,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0],[2,1,1],[2,2,0]]],"total_cube_count":11}],"canvas_size":[552,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2644","image_path":"images/combination3d_2644.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2644_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2644_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2644_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2644_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2644_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2644,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1]]],"total_cube_count":11}],"canvas_size":[574,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2645","image_path":"images/combination3d_2645.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2645_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2645_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2645_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_2645_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2645_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2645,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[552,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2646","image_path":"images/combination3d_2646.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2646_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2646_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2646_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2646_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2646_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2646,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,1,1],[1,1,1],[1,1,2],[2,0,2],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1],[1,0,2],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[595,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2647","image_path":"images/combination3d_2647.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2647_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2647_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2647_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_2647_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2647_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2647,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,2],[1,0,3],[2,0,3]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[597,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2648","image_path":"images/combination3d_2648.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2648_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2648_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2648_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2648_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2648_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2648,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,2,4],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[2,2,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":11}],"canvas_size":[566,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2649","image_path":"images/combination3d_2649.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2649_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2649_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2649_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2649_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2649_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2649,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[582,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2650","image_path":"images/combination3d_2650.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2650_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2650_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2650_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2650_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2650_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2650,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,3,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[1,2,1],[1,3,1],[2,0,0],[2,0,1],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[611,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2651","image_path":"images/combination3d_2651.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2651_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2651_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2651_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2651_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2651_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2651,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,1,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[558,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2652","image_path":"images/combination3d_2652.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2652_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2652_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2652_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_2652_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2652_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2652,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,1,0],[3,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":8}],"canvas_size":[552,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2653","image_path":"images/combination3d_2653.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2653_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2653_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2653_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_2653_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2653_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2653,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[2,0,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,1],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,0,2],[2,0,3],[3,0,3]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[605,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2654","image_path":"images/combination3d_2654.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2654_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2654_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2654_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2654_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2654_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2654,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0]]],"total_cube_count":11}],"canvas_size":[566,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2655","image_path":"images/combination3d_2655.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2655_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2655_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2655_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2655_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2655_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2655,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":10}],"canvas_size":[566,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2656","image_path":"images/combination3d_2656.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2656_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2656_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2656_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,5","question_id":"combination3d_2656_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2656_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2656,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[2,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,2],[2,1,0],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":10}],"canvas_size":[556,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2657","image_path":"images/combination3d_2657.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2657_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2657_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2657_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2657_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2657_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2657,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[2,0,0],[2,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[555,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2658","image_path":"images/combination3d_2658.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2658_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2658_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2658_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2658_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2658_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2658,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[614,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2659","image_path":"images/combination3d_2659.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2659_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2659_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2659_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2659_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2659_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2659,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[563,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2660","image_path":"images/combination3d_2660.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2660_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2660_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2660_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_2660_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2660_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2660,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,3],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[2,2,4]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,2],[2,1,2],[3,1,1],[3,1,2],[4,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[593,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2661","image_path":"images/combination3d_2661.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2661_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2661_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2661_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_2661_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2661_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2661,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,2,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,1],[2,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[3,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,4,0],[1,4,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11}],"canvas_size":[565,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2662","image_path":"images/combination3d_2662.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2662_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2662_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2662_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2662_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2662_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2662,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,1],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,1],[3,0,1],[3,1,1],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1],[3,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[2,1,3],[3,1,1],[3,1,2],[3,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[592,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2663","image_path":"images/combination3d_2663.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2663_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2663_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2663_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2663_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2663_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2663,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1],[3,1,2],[3,1,3],[3,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,1],[2,0,2],[2,0,3],[2,1,1],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,1],[1,4,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[599,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2664","image_path":"images/combination3d_2664.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2664_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2664_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2664_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2664_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2664_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2664,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[603,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2665","image_path":"images/combination3d_2665.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2665_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2665_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2665_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2665_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2665_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2665,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,2],[1,0,2],[1,1,0],[2,0,2],[3,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,0],[1,0,0],[1,0,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[1,2,1],[1,3,1],[2,1,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[2,0,0],[2,0,1],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[586,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2666","image_path":"images/combination3d_2666.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2666_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2666_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2666_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2666_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2666_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2666,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,3,2],[0,3,3],[0,4,0],[1,1,0],[1,1,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[4,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]]],"total_cube_count":8}],"canvas_size":[564,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2667","image_path":"images/combination3d_2667.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2667_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2667_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2667_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2667_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2667_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2667,"target_cube_count":8,"target_cubes":[[0,2,0],[1,2,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,2]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[588,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2668","image_path":"images/combination3d_2668.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2668_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2668_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2668_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2668_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2668_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2668,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,3,1]]],"total_cube_count":11}],"canvas_size":[585,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2669","image_path":"images/combination3d_2669.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2669_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2669_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2669_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2669_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2669_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2669,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,3,1],[1,0,2],[1,1,1],[2,1,1],[3,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,3,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,3],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,3,0],[2,1,0]]],"total_cube_count":15}],"canvas_size":[593,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2670","image_path":"images/combination3d_2670.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2670_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2670_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2670_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2670_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2670_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2670,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[1,3,3],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10}],"canvas_size":[564,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2671","image_path":"images/combination3d_2671.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2671_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2671_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2671_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2671_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2671_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2671,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[595,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2672","image_path":"images/combination3d_2672.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2672_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2672_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2672_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2672_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2672_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2672,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[577,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2673","image_path":"images/combination3d_2673.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2673_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2673_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2673_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2673_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2673_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2673,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[554,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2674","image_path":"images/combination3d_2674.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2674_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2674_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2674_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2674_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2674_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2674,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,3,0],[2,3,1],[2,3,2],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[3,1,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[553,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2675","image_path":"images/combination3d_2675.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2675_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2675_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2675_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2675_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2675_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2675,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[1,1,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,2,3],[3,0,3]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11}],"canvas_size":[582,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2676","image_path":"images/combination3d_2676.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2676_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2676_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2676_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2676_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2676_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2676,"target_cube_count":11,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[581,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2677","image_path":"images/combination3d_2677.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2677_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2677_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2677_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2677_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2677_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2677,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[2,4,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":9}],"canvas_size":[565,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2678","image_path":"images/combination3d_2678.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2678_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2678_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2678_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2678_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2678_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2678,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[0,3,1],[0,3,2],[0,3,3],[1,0,3],[1,1,3],[1,2,3],[1,3,3]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,1],[3,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,0,1],[3,0,2],[3,0,3],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,0,1],[3,0,2],[3,0,3],[3,0,4],[3,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[596,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2679","image_path":"images/combination3d_2679.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2679_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2679_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2679_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2679_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2679_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2679,"target_cube_count":13,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[3,0,0],[3,0,1],[3,0,2],[3,0,3],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]],[[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,2],[1,0,3],[1,1,2],[1,1,3],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[3,0,2],[3,0,3]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[616,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2680","image_path":"images/combination3d_2680.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2680_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2680_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2680_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2680_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2680_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2680,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,0,3],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,0,2],[2,1,2],[3,1,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,2,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[557,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2681","image_path":"images/combination3d_2681.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2681_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2681_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2681_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2681_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2681_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2681,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,4,0],[0,5,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[1,5,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[1,5,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,4],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,1,5],[1,1,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,3,1],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[556,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2682","image_path":"images/combination3d_2682.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2682_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2682_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2682_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2682_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2682_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2682,"target_cube_count":11,"target_cubes":[[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[1,5,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[607,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2683","image_path":"images/combination3d_2683.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2683_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2683_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2683_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2683_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2683_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2683,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[1,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12}],"canvas_size":[591,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2684","image_path":"images/combination3d_2684.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2684_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2684_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2684_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_2684_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2684_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2684,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[579,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2685","image_path":"images/combination3d_2685.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2685_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2685_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2685_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2685_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2685_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2685,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,0,2],[0,1,2],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12}],"canvas_size":[578,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2686","image_path":"images/combination3d_2686.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2686_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2686_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2686_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2686_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2686_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2686,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[608,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2687","image_path":"images/combination3d_2687.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2687_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2687_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2687_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2687_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2687_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2687,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,3,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[566,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2688","image_path":"images/combination3d_2688.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2688_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2688_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2688_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_2688_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2688_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2688,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[2,2,1],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[554,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2689","image_path":"images/combination3d_2689.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2689_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2689_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2689_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2689_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,5","question_id":"combination3d_2689_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2689,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[0,4,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,2,3]]],"total_cube_count":8}],"canvas_size":[593,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2690","image_path":"images/combination3d_2690.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2690_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2690_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2690_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2690_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2690_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2690,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0],[0,3,1],[0,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[595,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2691","image_path":"images/combination3d_2691.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2691_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2691_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2691_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2691_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2691_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2691,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[582,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2692","image_path":"images/combination3d_2692.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2692_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2692_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2692_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2692_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2692_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2692,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,1,0],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,0,2],[1,1,1],[2,1,1],[3,1,1],[3,2,0],[3,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[574,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2693","image_path":"images/combination3d_2693.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2693_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2693_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2693_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2693_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2693_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2693,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10}],"canvas_size":[588,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2694","image_path":"images/combination3d_2694.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2694_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2694_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2694_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2694_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2694_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2694,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,3,0],[3,2,0],[3,3,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":9}],"canvas_size":[598,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2695","image_path":"images/combination3d_2695.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2695_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2695_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2695_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2695_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2695_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2695,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,2,0],[1,2,0],[2,2,0],[2,3,0],[2,3,1],[3,0,0],[3,1,0],[3,2,0],[3,3,0],[3,4,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,2],[1,1,2],[2,0,3],[2,1,2],[2,1,3],[3,1,0],[3,1,1],[3,1,2],[3,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,2,0],[1,2,0],[2,2,0],[2,3,0],[2,3,1],[3,0,0],[3,1,0],[3,2,0],[3,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[611,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2696","image_path":"images/combination3d_2696.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2696_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2696_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2696_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2696_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2696_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2696,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[2,3,1],[3,0,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[592,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2697","image_path":"images/combination3d_2697.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2697_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2697_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2697_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2697_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2697_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2697,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,1],[2,1,0],[2,1,1],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[578,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2698","image_path":"images/combination3d_2698.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2698_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2698_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2698_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2698_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2698_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2698,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":9}],"canvas_size":[617,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2699","image_path":"images/combination3d_2699.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2699_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2699_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2699_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2699_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2699_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2699,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,1,1],[0,2,0],[0,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[580,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2700","image_path":"images/combination3d_2700.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2700_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2700_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2700_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2700_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2700_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2700,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9}],"canvas_size":[612,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2701","image_path":"images/combination3d_2701.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2701_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2701_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2701_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2701_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2701_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2701,"target_cube_count":9,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,2],[0,0,3],[1,0,0],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[2,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11}],"canvas_size":[571,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2702","image_path":"images/combination3d_2702.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2702_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2702_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2702_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_2702_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2702_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2702,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,1,1],[3,1,2],[3,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[0,3,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":12}],"canvas_size":[602,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2703","image_path":"images/combination3d_2703.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2703_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2703_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2703_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_2703_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2703_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2703,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,1,1],[1,2,0],[1,2,1],[2,2,1],[3,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,2],[0,1,0],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,2],[3,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0],[3,2,0]]],"total_cube_count":12}],"canvas_size":[565,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2704","image_path":"images/combination3d_2704.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2704_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2704_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2704_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2704_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2704_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2704,"target_cube_count":12,"target_cubes":[[0,0,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,1,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":9}],"canvas_size":[572,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2705","image_path":"images/combination3d_2705.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2705_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2705_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2705_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2705_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2705_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2705,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[579,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2706","image_path":"images/combination3d_2706.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2706_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2706_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2706_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2706_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2706_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2706,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,0,0],[2,1,1],[2,1,2],[3,0,0],[3,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[595,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2707","image_path":"images/combination3d_2707.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2707_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2707_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2707_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2707_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2707_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2707,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,2],[2,1,3]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[574,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2708","image_path":"images/combination3d_2708.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2708_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2708_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2708_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2708_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2708_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2708,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[4,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,2],[0,3,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[2,1,1],[2,2,0],[2,2,1],[2,3,1],[3,1,1],[4,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[572,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2709","image_path":"images/combination3d_2709.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2709_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2709_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2709_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2709_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2709_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2709,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,0,0],[3,0,1],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,1,1],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[614,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2710","image_path":"images/combination3d_2710.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2710_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2710_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2710_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2710_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2710_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2710,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,2,1],[2,2,1],[2,2,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[583,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2711","image_path":"images/combination3d_2711.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2711_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2711_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2711_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2711_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2711_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2711,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,1],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[1,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[585,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2712","image_path":"images/combination3d_2712.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2712_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2712_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2712_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2712_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_2712_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2712,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[3,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0]]],"total_cube_count":9}],"canvas_size":[611,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2713","image_path":"images/combination3d_2713.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2713_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2713_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2713_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2713_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2713_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2713,"target_cube_count":9,"target_cubes":[[0,0,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,2,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[2,0,1]]],"total_cube_count":13}],"canvas_size":[606,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2714","image_path":"images/combination3d_2714.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2714_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2714_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2714_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2714_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2714_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2714,"target_cube_count":13,"target_cubes":[[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[603,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2715","image_path":"images/combination3d_2715.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2715_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2715_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2715_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2715_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2715_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2715,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11}],"canvas_size":[550,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2716","image_path":"images/combination3d_2716.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2716_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2716_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2716_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2716_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2716_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2716,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,1],[1,1,2],[1,2,0],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,1],[2,3,1],[3,1,1],[3,2,1]]],"total_cube_count":13}],"canvas_size":[581,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2717","image_path":"images/combination3d_2717.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2717_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2717_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2717_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2717_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2717_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2717,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,1],[1,3,0],[1,3,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[577,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2718","image_path":"images/combination3d_2718.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2718_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2718_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2718_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2718_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_2718_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2718,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[620,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2719","image_path":"images/combination3d_2719.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2719_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2719_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2719_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2719_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2719_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2719,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1]],[[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12}],"canvas_size":[575,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2720","image_path":"images/combination3d_2720.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2720_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2720_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2720_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2720_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2720_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2720,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,3,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,3,0],[2,4,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,2]]],"total_cube_count":12}],"canvas_size":[619,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2721","image_path":"images/combination3d_2721.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2721_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2721_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2721_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2721_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2721_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2721,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[588,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2722","image_path":"images/combination3d_2722.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2722_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2722_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2722_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2722_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2722_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2722,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11}],"canvas_size":[564,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2723","image_path":"images/combination3d_2723.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2723_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2723_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2723_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2723_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2723_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2723,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[601,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2724","image_path":"images/combination3d_2724.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2724_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2724_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2724_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2724_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2724_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2724,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[1,4,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[1,4,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,2],[2,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,3],[0,1,4],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,3]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[609,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2725","image_path":"images/combination3d_2725.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2725_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2725_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2725_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2725_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2725_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2725,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[1,4,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":10}],"canvas_size":[571,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2726","image_path":"images/combination3d_2726.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2726_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2726_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2726_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2726_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2726_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2726,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[4,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,0,2],[1,2,0],[1,2,1]]],"total_cube_count":11}],"canvas_size":[586,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2727","image_path":"images/combination3d_2727.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2727_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2727_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2727_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2727_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_2727_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2727,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[3,1,0]]],"total_cube_count":10}],"canvas_size":[555,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2728","image_path":"images/combination3d_2728.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2728_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2728_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2728_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2728_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2728_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2728,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0]]],"total_cube_count":9}],"canvas_size":[567,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2729","image_path":"images/combination3d_2729.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2729_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2729_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2729_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2729_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2729_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2729,"target_cube_count":8,"target_cubes":[[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,0,2],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,1],[1,2,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":11}],"canvas_size":[552,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2730","image_path":"images/combination3d_2730.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2730_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2730_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2730_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2730_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_2730_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2730,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[1,0,3]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0]]],"total_cube_count":14}],"canvas_size":[561,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2731","image_path":"images/combination3d_2731.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2731_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2731_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2731_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2731_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2731_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2731,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[3,0,0],[3,0,1],[4,0,0],[4,0,1],[4,0,2],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[593,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2732","image_path":"images/combination3d_2732.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2732_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2732_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2732_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2732_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2732_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2732,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,2],[1,0,0],[1,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[561,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2733","image_path":"images/combination3d_2733.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2733_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2733_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2733_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2733_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_2733_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2733,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,0,2],[2,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,3,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[550,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2734","image_path":"images/combination3d_2734.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2734_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2734_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2734_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_2734_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2734_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2734,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[583,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2735","image_path":"images/combination3d_2735.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2735_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2735_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2735_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2735_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2735_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2735,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,2],[1,2,2]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[557,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2736","image_path":"images/combination3d_2736.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2736_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2736_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2736_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2736_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2736_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2736,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,3,2],[1,4,0],[1,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]]],"total_cube_count":12}],"canvas_size":[594,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2737","image_path":"images/combination3d_2737.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2737_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2737_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2737_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2737_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2737_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2737,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[600,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2738","image_path":"images/combination3d_2738.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2738_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2738_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2738_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_2738_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2738_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2738,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[2,0,2]]],"total_cube_count":10}],"canvas_size":[600,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2739","image_path":"images/combination3d_2739.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2739_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2739_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2739_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2739_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2739_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2739,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[609,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2740","image_path":"images/combination3d_2740.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2740_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2740_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2740_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_2740_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2740_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2740,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,1],[1,0,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[607,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2741","image_path":"images/combination3d_2741.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2741_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2741_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2741_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2741_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2741_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2741,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]]],"total_cube_count":14}],"canvas_size":[598,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2742","image_path":"images/combination3d_2742.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2742_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2742_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2742_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2742_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2742_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2742,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[575,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2743","image_path":"images/combination3d_2743.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2743_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2743_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2743_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2743_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2743_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2743,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[2,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":12}],"canvas_size":[592,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2744","image_path":"images/combination3d_2744.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2744_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2744_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2744_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2744_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2744_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2744,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[611,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2745","image_path":"images/combination3d_2745.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2745_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2745_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2745_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2745_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2745_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2745,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,5,0],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2],[2,0,2],[2,1,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11}],"canvas_size":[566,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2746","image_path":"images/combination3d_2746.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2746_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2746_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2746_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2746_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2746_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2746,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[580,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2747","image_path":"images/combination3d_2747.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2747_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2747_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2747_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_2747_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2747_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2747,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1],[2,0,2],[3,0,1],[4,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,3,2],[2,1,2],[2,2,2],[2,3,0],[2,3,1],[2,3,2]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[587,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2748","image_path":"images/combination3d_2748.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2748_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2748_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2748_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2748_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2748_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2748,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,3,0],[3,2,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1],[2,1,2],[2,1,3],[3,1,2]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[2,1,1],[2,2,1],[2,3,0],[2,3,1],[3,2,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[566,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2749","image_path":"images/combination3d_2749.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2749_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2749_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2749_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2749_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2749_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2749,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,2,0],[2,3,0],[3,2,0],[4,2,0],[4,2,1],[5,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,3,0],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[568,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2750","image_path":"images/combination3d_2750.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2750_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2750_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2750_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2750_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2750_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2750,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,1,2],[0,1,3],[1,0,2],[1,1,2],[2,1,2],[3,0,1],[3,1,0],[3,1,1],[3,1,2],[4,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,1,1],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[2,2,1],[2,3,1],[2,3,2],[2,4,0],[2,4,1],[3,4,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,4,0],[3,4,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,1],[3,1,1],[3,1,2],[4,1,0],[4,1,1],[4,1,2],[5,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14}],"canvas_size":[565,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2751","image_path":"images/combination3d_2751.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2751_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2751_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2751_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2751_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2751_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2751,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[2,4,0],[3,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[620,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2752","image_path":"images/combination3d_2752.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2752_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2752_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2752_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2752_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2752_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2752,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[1,0,2],[1,1,2],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[577,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2753","image_path":"images/combination3d_2753.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2753_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2753_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2753_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2753_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2753_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2753,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,2,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,3,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,3],[1,0,0]]],"total_cube_count":12}],"canvas_size":[592,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2754","image_path":"images/combination3d_2754.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2754_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2754_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2754_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2754_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2754_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2754,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[3,1,1],[3,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,1],[2,2,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[609,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2755","image_path":"images/combination3d_2755.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2755_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2755_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2755_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2755_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2755_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2755,"target_cube_count":12,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,1,0],[3,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,1],[1,0,1],[2,0,1],[2,0,2],[3,0,0],[3,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[612,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2756","image_path":"images/combination3d_2756.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2756_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2756_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2756_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2756_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2756_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2756,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[3,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,0,1],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[595,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2757","image_path":"images/combination3d_2757.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2757_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2757_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2757_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2757_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2757_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2757,"target_cube_count":10,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,2,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[2,1,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,4,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[588,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2758","image_path":"images/combination3d_2758.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2758_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2758_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2758_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_2758_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2758_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2758,"target_cube_count":11,"target_cubes":[[0,3,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[3,2,0],[3,2,1],[3,2,2],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,1,0],[0,2,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":10}],"canvas_size":[575,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2759","image_path":"images/combination3d_2759.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2759_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2759_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2759_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_2759_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2759_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2759,"target_cube_count":10,"target_cubes":[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,2,0],[4,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,2],[1,0,1],[1,1,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[1,2,1],[2,2,1],[2,2,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,2,0],[1,2,1],[1,3,1]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[579,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2760","image_path":"images/combination3d_2760.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2760_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2760_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2760_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2760_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2760_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2760,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,3,0],[0,4,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,4,0],[1,4,1],[1,4,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[571,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2761","image_path":"images/combination3d_2761.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2761_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2761_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2761_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2761_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2761_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2761,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,0],[0,3,1],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[570,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2762","image_path":"images/combination3d_2762.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2762_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2762_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2762_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2762_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2762_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2762,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[595,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2763","image_path":"images/combination3d_2763.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2763_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2763_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2763_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_2763_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2763_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2763,"target_cube_count":10,"target_cubes":[[0,4,0],[1,2,0],[1,3,0],[1,4,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14}],"canvas_size":[611,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2764","image_path":"images/combination3d_2764.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2764_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2764_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2764_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2764_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2764_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2764,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[558,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2765","image_path":"images/combination3d_2765.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2765_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2765_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2765_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2765_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2765_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2765,"target_cube_count":9,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,2,0],[2,2,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[612,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2766","image_path":"images/combination3d_2766.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2766_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2766_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2766_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2766_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2766_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2766,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0]]],"total_cube_count":9}],"canvas_size":[612,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2767","image_path":"images/combination3d_2767.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2767_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2767_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2767_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2767_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_2767_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2767,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,1],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[553,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2768","image_path":"images/combination3d_2768.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2768_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2768_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2768_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2768_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_2768_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2768,"target_cube_count":10,"target_cubes":[[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[571,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2769","image_path":"images/combination3d_2769.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2769_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2769_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2769_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_2769_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2769_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2769,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[564,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2770","image_path":"images/combination3d_2770.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2770_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2770_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2770_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2770_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2770_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2770,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[0,2,3],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[576,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2771","image_path":"images/combination3d_2771.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2771_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2771_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2771_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2771_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2771_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2771,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0],[3,1,1],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,1,3],[1,1,0],[1,1,1],[1,1,2],[2,0,2],[2,1,1],[2,1,2],[3,1,1],[3,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,2],[0,3,0],[0,3,1],[0,3,2],[1,0,2],[1,1,2],[1,2,2],[1,3,1],[1,3,2],[2,2,2],[2,3,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,0],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[606,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2772","image_path":"images/combination3d_2772.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2772_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2772_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2772_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2772_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2772_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2772,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,4,1]],[[0,1,0],[0,2,0],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":14}],"canvas_size":[573,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2773","image_path":"images/combination3d_2773.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2773_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2773_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2773_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2773_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2773_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2773,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[2,1,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1],[3,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":8}],"canvas_size":[610,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2774","image_path":"images/combination3d_2774.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2774_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2774_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2774_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2774_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2774_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2774,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12}],"canvas_size":[607,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2775","image_path":"images/combination3d_2775.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2775_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2775_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2775_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_2775_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2775_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2775,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2],[2,3,0],[2,3,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[0,1,3],[1,0,2],[1,1,2],[1,1,3],[2,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[595,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2776","image_path":"images/combination3d_2776.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2776_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2776_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2776_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2776_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2776_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2776,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[1,0,1],[1,0,2],[1,0,3],[1,1,1],[1,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,1,3],[0,2,1],[0,2,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[589,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2777","image_path":"images/combination3d_2777.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2777_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2777_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2777_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2777_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2777_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2777,"target_cube_count":12,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,2,1],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,1],[3,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[589,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2778","image_path":"images/combination3d_2778.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2778_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2778_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2778_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2778_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2778_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2778,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[577,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2779","image_path":"images/combination3d_2779.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2779_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2779_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2779_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2779_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2779_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2779,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[589,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2780","image_path":"images/combination3d_2780.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2780_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2780_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2780_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2780_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2780_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2780,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,3,0],[2,4,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0]]],"total_cube_count":10}],"canvas_size":[585,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2781","image_path":"images/combination3d_2781.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2781_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2781_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2781_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2781_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2781_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2781,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1],[1,0,2],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,1]]],"total_cube_count":12}],"canvas_size":[593,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2782","image_path":"images/combination3d_2782.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2782_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2782_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2782_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_2782_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2782_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2782,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,2],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,1],[2,1,1]]],"total_cube_count":13}],"canvas_size":[594,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2783","image_path":"images/combination3d_2783.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2783_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2783_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2783_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2783_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2783_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2783,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[564,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2784","image_path":"images/combination3d_2784.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2784_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2784_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2784_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2784_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2784_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2784,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,1],[0,1,1],[0,2,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,2,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":14}],"canvas_size":[592,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2785","image_path":"images/combination3d_2785.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2785_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2785_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2785_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2785_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2785_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2785,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10}],"canvas_size":[605,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2786","image_path":"images/combination3d_2786.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2786_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2786_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2786_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2786_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2786_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2786,"target_cube_count":10,"target_cubes":[[0,0,0],[0,3,0],[0,3,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,2],[0,4,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,1],[1,4,0],[1,4,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,1],[1,0,2],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[586,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2787","image_path":"images/combination3d_2787.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2787_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2787_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2787_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2787_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2787_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2787,"target_cube_count":12,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,3]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,2,0],[2,2,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[597,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2788","image_path":"images/combination3d_2788.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2788_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2788_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2788_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_2788_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2788_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2788,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[0,3,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0],[3,0,1],[3,0,2],[3,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[558,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2789","image_path":"images/combination3d_2789.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2789_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2789_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2789_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_2789_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2789_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2789,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,0,1],[3,1,1],[3,1,2],[4,1,2]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,3,0]],[[0,3,0],[1,3,0],[2,2,0],[2,3,0],[3,0,0],[3,1,0],[3,2,0],[3,3,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2],[3,1,3]]],"total_cube_count":15}],"canvas_size":[559,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2790","image_path":"images/combination3d_2790.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2790_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2790_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2790_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2790_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2790_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2790,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[0,2,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13}],"canvas_size":[588,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2791","image_path":"images/combination3d_2791.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2791_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2791_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2791_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2791_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2791_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2791,"target_cube_count":13,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[3,2,1],[3,2,2],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[566,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2792","image_path":"images/combination3d_2792.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2792_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2792_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2792_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2792_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2792_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2792,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[3,0,0],[3,0,1],[3,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,3,0],[2,0,0],[2,3,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,1,0],[3,0,1],[3,1,0],[3,1,1],[3,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13}],"canvas_size":[557,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2793","image_path":"images/combination3d_2793.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2793_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2793_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2793_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_2793_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2793_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2793,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0],[3,0,1],[3,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[555,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2794","image_path":"images/combination3d_2794.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2794_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2794_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2794_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,1","question_id":"combination3d_2794_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2794_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2794,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[598,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2795","image_path":"images/combination3d_2795.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2795_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2795_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2795_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2795_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2795_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2795,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,4,0],[1,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,0,1],[2,2,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1],[2,2,1],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[0,1,2],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]]],"total_cube_count":12}],"canvas_size":[581,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2796","image_path":"images/combination3d_2796.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2796_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2796_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2796_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2796_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2796_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2796,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[619,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2797","image_path":"images/combination3d_2797.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2797_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2797_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2797_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2797_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2797_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2797,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,1],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,2],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":14}],"canvas_size":[575,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2798","image_path":"images/combination3d_2798.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2798_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2798_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2798_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2798_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2798_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2798,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,1],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,3,2],[0,4,2]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,3,1],[0,4,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,2,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12}],"canvas_size":[574,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2799","image_path":"images/combination3d_2799.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2799_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2799_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2799_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2799_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2799_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2799,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,0,3]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,1,0],[4,1,1],[4,1,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,4,0],[2,4,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[4,0,0],[4,0,1],[4,0,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[618,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2800","image_path":"images/combination3d_2800.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2800_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2800_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2800_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,3","question_id":"combination3d_2800_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2800_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2800,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[3,0,1],[3,0,2],[4,0,0],[4,0,1],[4,0,2],[4,1,0],[4,1,1],[4,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[609,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2801","image_path":"images/combination3d_2801.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2801_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2801_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2801_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2801_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2801_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2801,"target_cube_count":10,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[3,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[2,1,1],[3,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[591,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2802","image_path":"images/combination3d_2802.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2802_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2802_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2802_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2802_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2802_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2802,"target_cube_count":13,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[1,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,3,0],[2,4,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":15}],"canvas_size":[588,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2803","image_path":"images/combination3d_2803.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2803_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2803_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2803_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2803_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2803_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2803,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3],[3,0,4],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[587,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2804","image_path":"images/combination3d_2804.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2804_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2804_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2804_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2804_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2804_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2804,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,2,0],[4,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,3,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1],[3,1,1],[3,1,2],[4,1,1]],[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,2,0],[4,1,0],[4,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":15}],"canvas_size":[567,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2805","image_path":"images/combination3d_2805.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2805_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2805_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2805_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2805_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2805_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2805,"target_cube_count":14,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,1,2],[3,2,0],[4,1,0],[4,1,1],[4,1,2],[4,1,3],[4,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]]],"total_cube_count":11}],"canvas_size":[555,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2806","image_path":"images/combination3d_2806.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2806_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2806_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2806_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2806_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2806_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2806,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[1,2,0]],[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[1,1,0]],[[0,1,0],[0,1,1],[0,2,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,2],[2,0,2],[2,1,2]]],"total_cube_count":13}],"canvas_size":[620,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2807","image_path":"images/combination3d_2807.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2807_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2807_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2807_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2807_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2807_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2807,"target_cube_count":13,"target_cubes":[[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,1]]],"total_cube_count":8}],"canvas_size":[569,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2808","image_path":"images/combination3d_2808.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2808_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2808_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2808_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2808_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2808_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2808,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[1,1,2],[1,2,2],[2,2,2]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":13}],"canvas_size":[565,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2809","image_path":"images/combination3d_2809.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2809_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2809_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2809_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2809_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2809_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2809,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,3,1],[1,4,0],[1,4,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,3,0],[1,4,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1],[0,4,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[599,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2810","image_path":"images/combination3d_2810.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2810_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2810_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2810_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2810_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2810_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2810,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[552,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2811","image_path":"images/combination3d_2811.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2811_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2811_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2811_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_2811_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2811_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2811,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[0,3,1],[0,4,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[564,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2812","image_path":"images/combination3d_2812.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2812_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2812_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2812_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2812_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2812_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2812,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[2,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[559,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2813","image_path":"images/combination3d_2813.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2813_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2813_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2813_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2813_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2813_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2813,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,2,0],[3,3,0],[3,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[606,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2814","image_path":"images/combination3d_2814.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2814_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2814_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2814_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2814_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2814_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2814,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1],[3,0,2]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,0,3],[1,1,2],[1,1,3]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,2,0],[1,3,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[600,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2815","image_path":"images/combination3d_2815.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2815_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2815_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2815_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2815_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2815_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2815,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0]]],"total_cube_count":10}],"canvas_size":[607,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2816","image_path":"images/combination3d_2816.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2816_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2816_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2816_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2816_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2816_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2816,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,1]],[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1]]],"total_cube_count":15}],"canvas_size":[615,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2817","image_path":"images/combination3d_2817.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2817_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2817_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2817_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2817_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_2817_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2817,"target_cube_count":14,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":8}],"canvas_size":[559,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2818","image_path":"images/combination3d_2818.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2818_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2818_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2818_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2818_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2818_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2818,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,1],[2,0,2],[2,0,3],[2,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[581,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2819","image_path":"images/combination3d_2819.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2819_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2819_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2819_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2819_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2819_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2819,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,2]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":14}],"canvas_size":[571,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2820","image_path":"images/combination3d_2820.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2820_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2820_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2820_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_2820_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2820_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2820,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,2]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,2,1],[2,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[602,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2821","image_path":"images/combination3d_2821.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2821_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2821_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2821_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2821_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2821_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2821,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,1],[1,2,1],[2,2,0],[2,2,1],[3,2,1],[4,0,0],[4,1,0],[4,2,0],[4,2,1],[5,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13}],"canvas_size":[600,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2822","image_path":"images/combination3d_2822.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2822_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2822_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2822_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2822_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2822_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2822,"target_cube_count":12,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[586,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2823","image_path":"images/combination3d_2823.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2823_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2823_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2823_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2823_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2823_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2823,"target_cube_count":8,"target_cubes":[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,1,0],[0,2,0],[0,2,1],[0,3,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]],[[0,1,0],[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,2,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":12}],"canvas_size":[574,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2824","image_path":"images/combination3d_2824.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2824_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2824_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2824_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2824_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2824_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2824,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,1,1],[3,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,2],[2,1,0],[2,1,1],[2,1,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[573,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2825","image_path":"images/combination3d_2825.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2825_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2825_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2825_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2825_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2825_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2825,"target_cube_count":10,"target_cubes":[[0,0,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,1],[1,1,1],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2]],[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[573,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2826","image_path":"images/combination3d_2826.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2826_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2826_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2826_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2826_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2826_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2826,"target_cube_count":11,"target_cubes":[[0,0,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[1,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[2,1,0],[2,2,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,1],[1,2,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,0],[2,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[2,0,1],[2,1,1],[3,0,1],[3,1,1],[4,0,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[564,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2827","image_path":"images/combination3d_2827.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2827_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2827_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2827_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2827_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2827_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2827,"target_cube_count":14,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0]]],"total_cube_count":8}],"canvas_size":[604,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2828","image_path":"images/combination3d_2828.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2828_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2828_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2828_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2828_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2828_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2828,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[0,3,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[582,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2829","image_path":"images/combination3d_2829.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2829_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2829_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2829_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2829_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2829_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2829,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,1,2],[0,1,3],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0],[3,2,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0],[3,2,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[0,3,2],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":14}],"canvas_size":[604,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2830","image_path":"images/combination3d_2830.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2830_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2830_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2830_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_2830_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2830_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2830,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0],[4,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[2,1,2],[2,1,3]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,0,1],[1,0,3],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13}],"canvas_size":[613,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2831","image_path":"images/combination3d_2831.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2831_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2831_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2831_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2831_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2831_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2831,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,4,0],[0,4,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[2,2,1],[2,2,2],[3,0,2],[3,1,1],[3,1,2],[3,1,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[556,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2832","image_path":"images/combination3d_2832.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2832_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2832_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2832_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2832_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2832_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2832,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,1,2],[2,0,1]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[3,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,1],[1,2,1],[1,3,1],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,3,0],[2,3,1],[3,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[561,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2833","image_path":"images/combination3d_2833.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2833_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2833_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2833_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2833_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2833_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2833,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,2,3],[1,0,2],[1,1,2],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[1,3,2],[1,4,1],[1,4,2],[2,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":15}],"canvas_size":[611,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2834","image_path":"images/combination3d_2834.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2834_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2834_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2834_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2834_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2834_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2834,"target_cube_count":14,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,1],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":8}],"canvas_size":[576,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2835","image_path":"images/combination3d_2835.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2835_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2835_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2835_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2835_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2835_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2835,"target_cube_count":8,"target_cubes":[[0,3,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[620,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2836","image_path":"images/combination3d_2836.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2836_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2836_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2836_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2836_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2836_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2836,"target_cube_count":9,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11}],"canvas_size":[588,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2837","image_path":"images/combination3d_2837.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2837_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2837_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2837_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2837_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2837_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2837,"target_cube_count":10,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[607,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2838","image_path":"images/combination3d_2838.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2838_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2838_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2838_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2838_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2838_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2838,"target_cube_count":8,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,2,1],[1,1,0],[1,2,1],[2,1,0],[2,1,1],[2,2,1],[3,0,1],[3,1,1],[3,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":15}],"canvas_size":[603,447],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2839","image_path":"images/combination3d_2839.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2839_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2839_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2839_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2839_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2839_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2839,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[594,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2840","image_path":"images/combination3d_2840.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2840_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2840_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2840_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2840_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2840_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2840,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,2,2],[0,2,3],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1]],[[0,0,1],[0,1,1],[1,0,1],[1,1,1],[1,1,2],[1,1,3],[1,2,1],[2,1,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,1],[2,1,1]]],"total_cube_count":13}],"canvas_size":[595,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2841","image_path":"images/combination3d_2841.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2841_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2841_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2841_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2841_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2841_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2841,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,1,1],[3,1,2],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[3,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,3,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[0,2,1],[1,2,1],[1,3,0],[1,3,1],[2,2,1]]],"total_cube_count":11}],"canvas_size":[550,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2842","image_path":"images/combination3d_2842.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2842_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2842_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2842_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2842_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2842_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2842,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[1,3,0],[2,2,0],[2,3,0],[2,3,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":8}],"canvas_size":[554,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2843","image_path":"images/combination3d_2843.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2843_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2843_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2843_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2843_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2843_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2843,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[606,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2844","image_path":"images/combination3d_2844.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2844_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2844_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2844_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2844_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2844_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2844,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1]],[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[574,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2845","image_path":"images/combination3d_2845.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2845_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2845_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2845_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2845_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2845_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2845,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,2],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1],[3,0,1],[3,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[597,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2846","image_path":"images/combination3d_2846.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2846_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2846_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2846_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2846_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2846_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2846,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,2,0],[3,2,1],[3,2,2],[3,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,2,0],[2,2,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0],[5,1,0],[5,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[5,0,0],[5,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,1],[3,0,0],[3,0,1],[4,0,0],[5,0,0],[5,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[550,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2847","image_path":"images/combination3d_2847.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2847_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2847_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2847_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2847_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2847_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2847,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0],[3,1,0],[4,0,0],[5,0,0],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9}],"canvas_size":[619,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2848","image_path":"images/combination3d_2848.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2848_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2848_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2848_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2848_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2848_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2848,"target_cube_count":9,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,1,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[606,449],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2849","image_path":"images/combination3d_2849.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2849_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2849_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2849_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2849_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2849_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2849,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,1,3]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,1,0],[3,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[1,2,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[2,1,1],[3,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":11}],"canvas_size":[552,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2850","image_path":"images/combination3d_2850.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2850_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2850_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2850_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2850_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2850_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2850,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,1,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,0,1],[2,0,2],[2,1,1],[2,1,2],[2,2,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,2],[1,1,1],[1,1,2],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1]]],"total_cube_count":14}],"canvas_size":[591,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2851","image_path":"images/combination3d_2851.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2851_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2851_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2851_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2851_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2851_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2851,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0]],[[0,0,2],[0,1,2],[0,2,1],[0,2,2],[0,3,1],[0,4,0],[0,4,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,2],[2,0,3],[2,0,4]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,2],[2,0,3],[2,0,4]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[556,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2852","image_path":"images/combination3d_2852.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2852_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2852_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2852_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2852_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2852_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2852,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2],[3,0,3],[3,0,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,1,2],[1,2,1],[2,1,1],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[1,2,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11}],"canvas_size":[570,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2853","image_path":"images/combination3d_2853.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2853_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2853_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2853_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,5","question_id":"combination3d_2853_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2853_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2853,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,1],[1,1,1],[1,1,2]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":12}],"canvas_size":[561,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2854","image_path":"images/combination3d_2854.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2854_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2854_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2854_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,3","question_id":"combination3d_2854_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2854_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2854,"target_cube_count":12,"target_cubes":[[0,3,0],[1,2,0],[1,2,1],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[3,1,2],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,3,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":10}],"canvas_size":[615,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2855","image_path":"images/combination3d_2855.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2855_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2855_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2855_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2855_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_2855_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2855,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[1,3,0],[1,3,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[619,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2856","image_path":"images/combination3d_2856.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2856_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2856_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2856_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_2856_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2856_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2856,"target_cube_count":8,"target_cubes":[[0,3,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[1,3,0],[2,3,0]]],"total_cube_count":10}],"canvas_size":[563,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2857","image_path":"images/combination3d_2857.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2857_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2857_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2857_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2857_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2857_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2857,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,3],[1,0,4]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[4,0,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[2,1,1],[3,0,0],[3,0,1],[3,1,1],[4,0,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10}],"canvas_size":[578,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2858","image_path":"images/combination3d_2858.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2858_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2858_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2858_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2858_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2858_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2858,"target_cube_count":9,"target_cubes":[[0,3,0],[1,3,0],[2,3,0],[3,1,0],[3,2,0],[3,3,0],[4,0,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":11}],"canvas_size":[612,465],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2859","image_path":"images/combination3d_2859.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2859_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2859_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2859_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,4","question_id":"combination3d_2859_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2859_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2859,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[563,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2860","image_path":"images/combination3d_2860.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2860_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2860_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2860_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2860_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2860_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2860,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,3]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0],[3,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[591,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2861","image_path":"images/combination3d_2861.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2861_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2861_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2861_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2861_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2861_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2861,"target_cube_count":9,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[3,2,0],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[4,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0],[4,0,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,1],[1,1,2],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]]],"total_cube_count":10}],"canvas_size":[576,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2862","image_path":"images/combination3d_2862.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2862_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2862_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2862_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2862_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2862_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2862,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[616,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2863","image_path":"images/combination3d_2863.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2863_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2863_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2863_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2863_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2863_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2863,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1]],[[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,1]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[2,1,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":13}],"canvas_size":[620,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2864","image_path":"images/combination3d_2864.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2864_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2864_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2864_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2864_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2864_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2864,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1]]],"total_cube_count":9}],"canvas_size":[567,461],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2865","image_path":"images/combination3d_2865.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2865_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2865_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2865_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2865_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2865_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2865,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[611,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2866","image_path":"images/combination3d_2866.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2866_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2866_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2866_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2866_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2866_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2866,"target_cube_count":10,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[555,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2867","image_path":"images/combination3d_2867.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2867_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2867_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2867_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2867_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_2867_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2867,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,1,1],[1,2,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2],[1,3,2]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,2,0]]],"total_cube_count":13}],"canvas_size":[611,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2868","image_path":"images/combination3d_2868.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2868_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2868_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2868_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2868_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2868_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2868,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2],[1,4,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":13}],"canvas_size":[612,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2869","image_path":"images/combination3d_2869.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2869_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2869_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2869_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2869_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2869_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2869,"target_cube_count":12,"target_cubes":[[0,1,0],[0,5,0],[0,5,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[1,4,0],[1,5,0],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[2,0,0],[2,0,1]],[[0,1,0],[0,1,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[603,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2870","image_path":"images/combination3d_2870.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2870_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2870_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2870_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2870_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2870_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2870,"target_cube_count":13,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[557,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2871","image_path":"images/combination3d_2871.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2871_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2871_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2871_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2871_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2871_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2871,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2],[2,1,2]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,2,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,1,1],[2,1,2],[3,1,2]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1]]],"total_cube_count":14}],"canvas_size":[550,464],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2872","image_path":"images/combination3d_2872.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2872_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2872_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2872_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2872_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2872_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2872,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[1,3,2],[1,3,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":8}],"canvas_size":[589,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2873","image_path":"images/combination3d_2873.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2873_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2873_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2873_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2873_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2873_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2873,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[0,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[2,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,2,0],[2,2,0]]],"total_cube_count":11}],"canvas_size":[573,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2874","image_path":"images/combination3d_2874.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2874_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2874_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2874_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2874_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2874_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2874,"target_cube_count":10,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[0,3,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[572,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2875","image_path":"images/combination3d_2875.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2875_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2875_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2875_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2875_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2875_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2875,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,0],[3,0,1],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,2,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":13}],"canvas_size":[619,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2876","image_path":"images/combination3d_2876.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2876_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2876_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2876_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_2876_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2876_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2876,"target_cube_count":13,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,2,0],[3,2,0],[3,3,0],[4,2,0],[4,3,0],[4,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0],[4,0,1],[5,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[2,1,2]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,2],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0],[4,0,0],[4,0,1],[5,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,5,0],[1,4,0]]],"total_cube_count":14}],"canvas_size":[598,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2877","image_path":"images/combination3d_2877.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2877_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2877_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2877_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2877_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2877_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2877,"target_cube_count":14,"target_cubes":[[0,2,0],[1,2,0],[2,1,0],[2,1,1],[2,2,0],[3,0,0],[3,0,1],[3,0,2],[3,1,0],[3,2,0],[4,1,0],[4,2,0],[4,2,1],[5,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[1,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[569,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2878","image_path":"images/combination3d_2878.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2878_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2878_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2878_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2878_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2878_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2878,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2],[1,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[553,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2879","image_path":"images/combination3d_2879.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2879_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2879_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2879_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2879_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2879_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2879,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0],[2,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[2,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[0,2,1]]],"total_cube_count":9}],"canvas_size":[612,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2880","image_path":"images/combination3d_2880.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2880_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2880_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2880_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,2","question_id":"combination3d_2880_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2880_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2880,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2]],[[0,0,1],[0,0,2],[0,1,1],[0,2,1],[0,3,1],[0,4,1],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,1,0],[1,1,0],[2,1,0],[3,1,0],[4,0,0],[4,0,1],[4,1,0],[4,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,0,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":14}],"canvas_size":[553,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2881","image_path":"images/combination3d_2881.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2881_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2881_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2881_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2881_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2881_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2881,"target_cube_count":14,"target_cubes":[[0,2,0],[0,2,1],[1,2,0],[1,3,0],[1,3,1],[1,3,2],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0],[2,4,0],[3,0,0],[3,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[569,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2882","image_path":"images/combination3d_2882.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2882_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2882_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2882_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2882_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2882_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2882,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8}],"canvas_size":[580,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2883","image_path":"images/combination3d_2883.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2883_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2883_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2883_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2883_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2883_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2883,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[2,0,1],[2,1,1],[2,2,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,3],[1,0,2],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,2,2],[1,2,3],[2,1,3],[2,2,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,3,0],[2,3,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[567,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2884","image_path":"images/combination3d_2884.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2884_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2884_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2884_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2884_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2884_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2884,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,0,1]],[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,0,2],[1,1,1],[2,0,2]],[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,1,2]],[[0,1,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,0,1],[2,0,2],[2,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,1]]],"total_cube_count":14}],"canvas_size":[557,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2885","image_path":"images/combination3d_2885.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2885_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2885_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2885_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,2","question_id":"combination3d_2885_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2885_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2885,"target_cube_count":14,"target_cubes":[[0,2,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,1,0],[3,2,0],[3,2,1],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[2,0,1]],[[0,1,1],[0,2,1],[0,2,2],[1,0,1],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":14}],"canvas_size":[585,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2886","image_path":"images/combination3d_2886.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2886_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2886_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2886_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2886_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2886_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2886,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[3,2,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[562,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2887","image_path":"images/combination3d_2887.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2887_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2887_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2887_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2887_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2887_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2887,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,1],[0,4,1],[0,4,2],[1,2,1],[1,4,2]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,1,2],[3,1,1],[4,1,1],[4,2,1],[4,2,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[4,1,0],[4,2,0],[4,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[587,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2888","image_path":"images/combination3d_2888.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2888_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2888_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2888_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,2","question_id":"combination3d_2888_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2888_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2888,"target_cube_count":12,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[3,1,0],[4,0,0],[4,0,1],[4,1,0],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[583,455],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2889","image_path":"images/combination3d_2889.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2889_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2889_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2889_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2889_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2889_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2889,"target_cube_count":8,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":8}],"canvas_size":[583,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2890","image_path":"images/combination3d_2890.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2890_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2890_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2890_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2890_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2890_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2890,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,2,0],[1,2,1],[1,2,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]]],"total_cube_count":11}],"canvas_size":[597,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2891","image_path":"images/combination3d_2891.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2891_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2891_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2891_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2891_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2891_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2891,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,1,1],[1,1,1],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[602,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2892","image_path":"images/combination3d_2892.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2892_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2892_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2892_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2892_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2892_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2892,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,1,2]],[[0,1,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,1,0],[2,1,1]]],"total_cube_count":13}],"canvas_size":[579,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2893","image_path":"images/combination3d_2893.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2893_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2893_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2893_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_2893_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2893_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2893,"target_cube_count":13,"target_cubes":[[0,2,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[0,2,2],[0,3,1],[1,1,1],[2,1,1],[3,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,3,0],[2,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1]],[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,3,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,2,2],[2,0,1],[2,1,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":13}],"canvas_size":[573,479],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2894","image_path":"images/combination3d_2894.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2894_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2894_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2894_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2894_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,5","question_id":"combination3d_2894_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2894,"target_cube_count":13,"target_cubes":[[0,2,0],[0,3,0],[0,3,1],[0,3,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,3,0],[1,3,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0],[2,1,0],[3,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":10}],"canvas_size":[563,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2895","image_path":"images/combination3d_2895.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2895_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2895_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2895_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,2","question_id":"combination3d_2895_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2895_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2895,"target_cube_count":10,"target_cubes":[[0,0,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[603,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2896","image_path":"images/combination3d_2896.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2896_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2896_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2896_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2896_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2896_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2896,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,3,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1],[2,1,1],[3,1,0],[3,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,2],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":9}],"canvas_size":[579,436],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2897","image_path":"images/combination3d_2897.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2897_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2897_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2897_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2897_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2897_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2897,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]],[[0,0,2],[0,1,2],[0,2,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":11}],"canvas_size":[571,431],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2898","image_path":"images/combination3d_2898.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2898_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2898_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2898_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2898_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2898_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2898,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[0,2,2],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[617,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2899","image_path":"images/combination3d_2899.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2899_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2899_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2899_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,3","question_id":"combination3d_2899_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2899_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2899,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[586,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2900","image_path":"images/combination3d_2900.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2900_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2900_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2900_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,1","question_id":"combination3d_2900_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2900_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2900,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,2],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[563,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2901","image_path":"images/combination3d_2901.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2901_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2901_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2901_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2901_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2901_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2901,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[3,0,0],[3,0,1],[3,0,2],[3,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2],[3,0,2]],[[0,0,0],[0,0,1],[1,0,0],[2,0,0]]],"total_cube_count":12}],"canvas_size":[579,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2902","image_path":"images/combination3d_2902.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2902_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2902_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2902_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,4","question_id":"combination3d_2902_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2902_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2902,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[1,1,1]]],"total_cube_count":8}],"canvas_size":[563,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2903","image_path":"images/combination3d_2903.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2903_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2903_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2903_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2903_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2903_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2903,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[597,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2904","image_path":"images/combination3d_2904.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2904_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2904_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2904_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2904_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2904_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2904,"target_cube_count":8,"target_cubes":[[0,2,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,1],[2,1,1],[2,2,0],[2,2,1]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,2],[2,1,2]]],"total_cube_count":14}],"canvas_size":[571,471],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2905","image_path":"images/combination3d_2905.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2905_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2905_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2905_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2905_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2905_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2905,"target_cube_count":14,"target_cubes":[[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,1,1],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,3,2]],[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,3],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13}],"canvas_size":[565,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2906","image_path":"images/combination3d_2906.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2906_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2906_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2906_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2906_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2906_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2906,"target_cube_count":13,"target_cubes":[[0,3,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,0,0],[2,2,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1]]],"total_cube_count":10}],"canvas_size":[619,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2907","image_path":"images/combination3d_2907.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2907_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2907_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2907_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,4","question_id":"combination3d_2907_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2907_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2907,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10}],"canvas_size":[598,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2908","image_path":"images/combination3d_2908.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2908_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2908_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2908_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2908_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_2908_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2908,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,1,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":12}],"canvas_size":[579,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2909","image_path":"images/combination3d_2909.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2909_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2909_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2909_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2909_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2909_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2909,"target_cube_count":11,"target_cubes":[[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,0,1],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,3,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[3,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[0,3,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,1,0],[1,1,1],[1,2,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0]]],"total_cube_count":13}],"canvas_size":[552,438],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2910","image_path":"images/combination3d_2910.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2910_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2910_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2910_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_2910_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2910_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2910,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,3,0],[0,4,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,1,1],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[610,463],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2911","image_path":"images/combination3d_2911.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2911_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2911_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2911_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2911_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2911_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2911,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,1]],[[0,0,1],[0,1,1],[0,2,1],[0,3,0],[0,3,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,0,1],[1,0,1],[2,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":11}],"canvas_size":[555,430],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2912","image_path":"images/combination3d_2912.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2912_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2912_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2912_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2912_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2912_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2912,"target_cube_count":11,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,0,2],[3,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[1,1,0],[1,2,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9}],"canvas_size":[586,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2913","image_path":"images/combination3d_2913.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2913_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2913_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2913_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2913_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2913_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2913,"target_cube_count":9,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[1,0,0],[1,1,0],[1,2,0]],[[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12}],"canvas_size":[616,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2914","image_path":"images/combination3d_2914.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2914_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2914_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2914_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2914_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,6","question_id":"combination3d_2914_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2914,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,3,0]]],"total_cube_count":8}],"canvas_size":[600,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2915","image_path":"images/combination3d_2915.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2915_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2915_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2915_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2915_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,2","question_id":"combination3d_2915_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2915,"target_cube_count":8,"target_cubes":[[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,5,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[612,434],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2916","image_path":"images/combination3d_2916.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2916_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2916_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2916_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2916_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2916_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2916,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1],[1,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[560,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2917","image_path":"images/combination3d_2917.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2917_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2917_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2917_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2917_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2917_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2917,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,1]],[[0,0,0],[0,0,1],[1,0,1],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10}],"canvas_size":[557,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2918","image_path":"images/combination3d_2918.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2918_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2918_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2918_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2918_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2918_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2918,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,2,1],[1,2,2]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,1],[1,3,1]],[[0,0,0],[0,0,1],[0,1,1],[0,2,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[3,2,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0]]],"total_cube_count":12}],"canvas_size":[564,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2919","image_path":"images/combination3d_2919.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2919_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2919_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2919_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2919_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2919_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2919,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,2,0],[2,3,0],[2,4,0],[2,5,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,1],[0,1,2],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,0,2],[0,1,1],[1,1,1],[1,2,0],[1,2,1],[2,2,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":8}],"canvas_size":[607,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2920","image_path":"images/combination3d_2920.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2920_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2920_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2920_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2920_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2920_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2920,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[1,1,0],[1,2,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1],[3,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]]],"total_cube_count":12}],"canvas_size":[558,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2921","image_path":"images/combination3d_2921.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2921_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2921_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2921_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2921_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2921_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2921,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[1,2,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[2,0,1]]],"total_cube_count":8}],"canvas_size":[551,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2922","image_path":"images/combination3d_2922.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2922_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2922_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2922_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2922_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2922_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2922,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1],[4,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]],[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[550,444],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2923","image_path":"images/combination3d_2923.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2923_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2923_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2923_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2923_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2923_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2923,"target_cube_count":13,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4],[2,2,0],[2,2,1],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14}],"canvas_size":[601,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2924","image_path":"images/combination3d_2924.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2924_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2924_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2924_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2924_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2924_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2924,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,2],[1,1,0],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[2,0,1],[2,0,2],[2,1,1],[2,1,2],[3,0,0],[3,0,1],[3,1,1],[3,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":14}],"canvas_size":[583,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2925","image_path":"images/combination3d_2925.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2925_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2925_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2925_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2925_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2925_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2925,"target_cube_count":14,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0]],[[0,0,1],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1]]],"total_cube_count":12}],"canvas_size":[605,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2926","image_path":"images/combination3d_2926.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2926_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2926_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2926_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2926_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2926_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2926,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":9}],"canvas_size":[554,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2927","image_path":"images/combination3d_2927.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2927_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2927_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2927_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2927_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2927_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2927,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,2],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":12}],"canvas_size":[594,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2928","image_path":"images/combination3d_2928.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2928_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2928_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2928_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2928_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2928_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2928,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,2,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0]],[[0,0,0],[1,0,0],[1,0,1]],[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]]],"total_cube_count":15},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":14}],"canvas_size":[584,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2929","image_path":"images/combination3d_2929.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2929_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2929_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2929_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2929_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2929_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2929,"target_cube_count":14,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[2,2,2],[2,2,3],[3,1,0],[3,2,0],[4,0,0],[4,1,0],[5,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[610,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2930","image_path":"images/combination3d_2930.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2930_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2930_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2930_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2930_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2930_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2930,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,0,0],[1,0,1],[1,1,0],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1],[1,1,1],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,3,1],[1,3,0],[1,3,1]],[[0,0,0],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,1,0]]],"total_cube_count":12}],"canvas_size":[593,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2931","image_path":"images/combination3d_2931.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2931_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2931_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2931_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2931_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_2931_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2931,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]],[[0,1,0],[0,1,1],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,1],[1,0,1],[1,0,2],[2,0,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[594,421],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2932","image_path":"images/combination3d_2932.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2932_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2932_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2932_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2932_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2932_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2932,"target_cube_count":10,"target_cubes":[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,1,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4]],[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":14}],"canvas_size":[587,426],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2933","image_path":"images/combination3d_2933.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2933_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2933_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2933_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_2933_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2933_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2933,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0]],[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0]],[[0,1,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,2,1],[1,2,1],[2,0,0],[2,1,0],[2,2,0],[2,2,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,2],[1,3,2]]],"total_cube_count":14}],"canvas_size":[598,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2934","image_path":"images/combination3d_2934.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2934_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2934_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2934_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,3","question_id":"combination3d_2934_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2934_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2934,"target_cube_count":14,"target_cubes":[[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,1,0],[3,1,0],[4,0,0],[4,0,1],[4,0,2],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[2,2,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,2,1],[1,2,2],[2,2,2]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[2,2,0]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[575,470],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2935","image_path":"images/combination3d_2935.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2935_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2935_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2935_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_2935_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2935_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2935,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,1,0],[1,2,0],[2,2,0],[2,2,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0],[5,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[2,0,3]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,1,0],[1,1,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[576,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2936","image_path":"images/combination3d_2936.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2936_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2936_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2936_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2936_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2936_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2936,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0],[4,2,0],[4,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,1,0],[0,1,1],[0,1,2],[1,0,2],[1,1,2],[1,1,3]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[2,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[602,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2937","image_path":"images/combination3d_2937.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2937_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2937_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2937_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2937_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2937_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2937,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,2],[0,3,2]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[0,3,0],[1,1,0],[2,0,0],[2,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,1,0],[0,2,0],[0,3,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":11}],"canvas_size":[560,475],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2938","image_path":"images/combination3d_2938.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2938_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2938_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2938_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"10,1","question_id":"combination3d_2938_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2938_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2938,"target_cube_count":10,"target_cubes":[[0,2,0],[1,2,0],[2,1,0],[2,2,0],[2,3,0],[3,1,0],[3,2,0],[4,0,0],[4,1,0],[4,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,2,1],[1,0,1],[1,1,1],[1,2,1]],[[0,1,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[2,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,2]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":15},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,2]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":14}],"canvas_size":[612,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2939","image_path":"images/combination3d_2939.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2939_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2939_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2939_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2939_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2939_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2939,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,3,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,1],[1,2,1],[2,1,1],[2,2,0],[2,2,1],[2,3,1],[2,3,2]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,1],[1,0,2],[1,1,1],[1,1,2],[2,0,2],[2,1,2]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":13}],"canvas_size":[599,422],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2940","image_path":"images/combination3d_2940.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2940_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2940_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2940_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_2940_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2940_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2940,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,1,1],[2,2,0],[2,2,1],[3,0,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,1],[0,2,2],[1,1,1],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,2,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,1],[0,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[606,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2941","image_path":"images/combination3d_2941.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2941_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2941_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2941_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2941_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2941_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2941,"target_cube_count":11,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1],[4,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[1,0,1],[1,0,2],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[0,2,0],[1,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[1,0,1],[1,1,1],[1,1,2],[2,0,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":12}],"canvas_size":[601,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2942","image_path":"images/combination3d_2942.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2942_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2942_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2942_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2942_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2942_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2942,"target_cube_count":12,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,1,0],[3,2,0],[4,0,0],[4,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8}],"canvas_size":[615,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2943","image_path":"images/combination3d_2943.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2943_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2943_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2943_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2943_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2943_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2943,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[552,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2944","image_path":"images/combination3d_2944.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2944_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2944_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2944_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2944_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_2944_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2944,"target_cube_count":8,"target_cubes":[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,2,2],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":8}],"canvas_size":[589,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2945","image_path":"images/combination3d_2945.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2945_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2945_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2945_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2945_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2945_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2945,"target_cube_count":8,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,0,1],[2,1,0],[2,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,2,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[2,1,0],[2,2,0],[2,2,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,1],[0,1,1],[1,1,1],[1,2,1],[2,1,1],[2,2,0],[2,2,1],[2,2,2]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":10}],"canvas_size":[595,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2946","image_path":"images/combination3d_2946.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2946_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2946_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2946_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2946_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2946_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2946,"target_cube_count":10,"target_cubes":[[0,0,0],[0,1,0],[1,1,0],[1,2,0],[1,3,0],[2,1,0],[2,2,0],[2,2,1],[2,3,0],[2,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,1],[2,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,1,0],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12}],"canvas_size":[581,457],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2947","image_path":"images/combination3d_2947.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2947_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2947_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2947_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2947_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2947_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2947,"target_cube_count":11,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,3],[1,0,1],[2,0,1],[3,0,1],[4,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,3,0],[0,4,0],[0,4,1],[1,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,3,0],[0,4,0],[1,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[585,437],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2948","image_path":"images/combination3d_2948.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2948_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2948_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2948_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"12,5","question_id":"combination3d_2948_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2948_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2948,"target_cube_count":12,"target_cubes":[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,3,0],[0,4,0],[1,3,0],[1,3,1],[1,3,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[1,3,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,1,2],[0,2,1],[1,1,0],[1,1,1],[1,1,2],[1,2,1],[1,2,2],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,2],[1,1,1],[1,1,2]],[[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,1,1]]],"total_cube_count":11}],"canvas_size":[606,443],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2949","image_path":"images/combination3d_2949.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2949_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2949_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2949_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,2","question_id":"combination3d_2949_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2949_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2949,"target_cube_count":11,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,1],[0,1,1],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":10}],"canvas_size":[590,445],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2950","image_path":"images/combination3d_2950.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2950_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2950_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2950_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2950_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2950_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2950,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8}],"canvas_size":[581,448],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2951","image_path":"images/combination3d_2951.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2951_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2951_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2951_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2951_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2951_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2951,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,1,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8}],"canvas_size":[565,423],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2952","image_path":"images/combination3d_2952.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2952_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2952_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2952_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2952_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2952_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2952,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,2,0],[2,3,0],[3,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1],[2,0,2]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,0,0]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":12}],"canvas_size":[599,474],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2953","image_path":"images/combination3d_2953.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2953_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2953_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2953_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2953_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2953_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2953,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1],[0,3,2]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1],[1,1,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,3,0],[0,3,1]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1],[1,1,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[3,1,0]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,0,3],[1,1,1],[1,1,2],[1,1,3],[2,0,2],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14}],"canvas_size":[561,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2954","image_path":"images/combination3d_2954.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2954_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2954_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2954_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2954_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2954_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2954,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0],[1,2,0],[2,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,1],[1,0,2],[1,0,3]]],"total_cube_count":10}],"canvas_size":[555,460],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2955","image_path":"images/combination3d_2955.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2955_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2955_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2955_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2955_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,2","question_id":"combination3d_2955_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2955,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[1,2,1],[2,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[3,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,0,0],[1,1,2]],[[0,0,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,2,0],[1,2,1]],[[0,0,0],[0,0,1]]],"total_cube_count":8}],"canvas_size":[555,435],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2956","image_path":"images/combination3d_2956.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2956_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2956_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2956_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2956_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2956_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2956,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[1,2,0],[1,3,0],[1,3,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[2,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]],[[0,0,2],[1,0,0],[1,0,1],[1,0,2],[2,0,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,1,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9}],"canvas_size":[553,442],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2957","image_path":"images/combination3d_2957.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2957_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2957_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2957_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2957_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,4","question_id":"combination3d_2957_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2957,"target_cube_count":9,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[597,466],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2958","image_path":"images/combination3d_2958.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2958_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2958_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2958_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,2","question_id":"combination3d_2958_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2958_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2958,"target_cube_count":8,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[2,2,1],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,0],[1,0,1]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1]],[[0,0,2],[1,0,2],[1,1,0],[1,1,1],[1,1,2]]],"total_cube_count":8}],"canvas_size":[591,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2959","image_path":"images/combination3d_2959.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2959_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2959_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2959_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2959_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2959_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2959,"target_cube_count":8,"target_cubes":[[0,1,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,1,1],[1,0,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,3,0],[2,4,0],[2,4,1],[2,4,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,2,0],[0,2,3],[0,2,4],[1,2,4]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[2,0,0],[2,3,0],[2,4,0],[2,4,1]],[[0,0,0],[0,1,0]]],"total_cube_count":11}],"canvas_size":[558,451],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2960","image_path":"images/combination3d_2960.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2960_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2960_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2960_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2960_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2960_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2960,"target_cube_count":11,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[1,5,0],[2,0,0],[2,3,0],[2,4,0],[2,4,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,1,0],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[2,2,0]],[[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[1,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,2]]],"total_cube_count":10}],"canvas_size":[590,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2961","image_path":"images/combination3d_2961.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2961_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2961_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2961_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2961_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2961_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2961,"target_cube_count":10,"target_cubes":[[0,1,0],[1,1,0],[1,1,1],[2,1,0],[3,0,0],[3,1,0],[4,1,0],[4,2,0],[5,2,0],[5,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[1,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,1,0],[1,1,1]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0]],[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0]]],"total_cube_count":10}],"canvas_size":[569,458],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2962","image_path":"images/combination3d_2962.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2962_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2962_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2962_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2962_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,3","question_id":"combination3d_2962_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2962,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8}],"canvas_size":[553,472],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2963","image_path":"images/combination3d_2963.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2963_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2963_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2963_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2963_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,3","question_id":"combination3d_2963_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2963,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,1,0],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[1,0,0],[2,0,0]],[[0,1,1],[1,1,1],[2,0,1],[2,1,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,1],[1,0,2],[1,1,1],[2,0,0],[2,0,1],[2,1,1],[3,0,1],[3,1,1],[4,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[2,0,2]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":15},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,2]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1]]],"total_cube_count":14}],"canvas_size":[555,468],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2964","image_path":"images/combination3d_2964.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2964_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2964_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2964_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2964_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2964_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2964,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,0,4],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,0,0],[2,0,1],[2,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[0,3,0],[0,3,1],[0,4,0],[0,4,1],[1,1,1],[1,2,1],[2,0,1],[2,1,1],[2,2,1],[2,3,1],[2,4,1]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0],[2,1,0],[3,1,0],[3,1,1],[4,0,0],[4,0,1],[4,1,0],[4,1,1],[5,1,0],[5,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,2],[1,1,3],[2,0,4],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],[[0,0,0],[0,0,1]]],"total_cube_count":15}],"canvas_size":[576,433],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2965","image_path":"images/combination3d_2965.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2965_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2965_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2965_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2965_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,6","question_id":"combination3d_2965_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2965,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8}],"canvas_size":[607,476],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_2966","image_path":"images/combination3d_2966.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2966_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2966_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2966_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2966_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2966_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2966,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,3],[0,2,3],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,3],[1,2,4],[1,3,3],[2,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,1,1],[1,2,1],[2,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[3,0,0]]],"total_cube_count":13}],"canvas_size":[563,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2967","image_path":"images/combination3d_2967.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2967_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2967_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2967_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_2967_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2967_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2967,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[0,2,2],[0,3,0],[0,3,1],[1,1,0],[1,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,1],[2,0,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1],[1,1,1],[1,2,1],[1,2,2]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,3,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[557,478],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2968","image_path":"images/combination3d_2968.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2968_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2968_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2968_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2968_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,6","question_id":"combination3d_2968_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2968,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,0],[0,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3]]],"total_cube_count":10}],"canvas_size":[615,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2969","image_path":"images/combination3d_2969.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2969_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2969_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2969_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2969_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_2969_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2969,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0],[4,0,0]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,0,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[2,0,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,1],[0,1,2],[0,2,2],[1,0,3],[2,0,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[2,0,0],[2,1,0],[3,1,0],[3,1,1]],[[0,0,1],[0,1,1],[1,1,0],[1,1,1],[1,2,1]]],"total_cube_count":14}],"canvas_size":[599,429],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2970","image_path":"images/combination3d_2970.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2970_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2970_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2970_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2970_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,5","question_id":"combination3d_2970_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2970,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,0,1],[1,0,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[0,1,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,1,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0],[1,0,1],[2,0,0]]],"total_cube_count":8}],"canvas_size":[557,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2971","image_path":"images/combination3d_2971.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2971_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2971_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2971_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,4","question_id":"combination3d_2971_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2971_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2971,"target_cube_count":8,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,2,1],[0,2,2],[0,2,3],[0,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,2],[0,2,2],[1,0,2],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,2,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0],[2,2,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[561,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2972","image_path":"images/combination3d_2972.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2972_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2972_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2972_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2972_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2972_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2972,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[1,3,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,2,0],[4,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,4],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[0,2,1],[0,2,2],[1,0,4],[1,1,2],[1,1,3]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[3,1,0],[3,1,1],[3,2,0],[4,1,0],[4,2,0],[5,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":13}],"canvas_size":[605,462],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2973","image_path":"images/combination3d_2973.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2973_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2973_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2973_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,2","question_id":"combination3d_2973_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2973_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2973,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,1,0],[1,1,1],[2,0,0],[2,1,0],[2,1,1],[2,2,0],[3,1,0],[3,2,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]]],"total_cube_count":14},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,1,0],[1,1,1],[2,0,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[1,0,0],[1,1,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,2],[1,0,0],[1,0,1],[1,1,1],[1,1,2],[2,0,0],[3,0,0]],[[0,0,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1]]],"total_cube_count":15}],"canvas_size":[554,432],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2974","image_path":"images/combination3d_2974.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2974_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2974_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2974_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2974_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,4","question_id":"combination3d_2974_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2974,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,1],[0,4,1],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[1,4,1],[2,4,0],[2,4,1]],[[0,1,0],[0,2,0],[1,0,0],[1,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,1,2],[1,1,1],[2,0,1],[2,1,0],[2,1,1]],[[0,0,0],[1,0,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1]]],"total_cube_count":13},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,2,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1]]],"total_cube_count":14}],"canvas_size":[601,456],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2975","image_path":"images/combination3d_2975.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2975_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2975_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2975_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,5","question_id":"combination3d_2975_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2975_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2975,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,0],[1,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[1,1,0],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[1,0,0],[1,0,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[589,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2976","image_path":"images/combination3d_2976.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2976_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2976_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2976_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2976_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,5","question_id":"combination3d_2976_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2976,"target_cube_count":11,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[2,0,0],[2,0,1],[2,0,2],[2,0,3]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,1,1],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[2,2,0],[3,0,1],[3,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0],[2,0,1],[2,0,2]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,1,0],[0,2,0]],[[0,2,0],[1,2,0],[2,0,0],[2,1,0],[2,2,0]]],"total_cube_count":12}],"canvas_size":[606,459],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2977","image_path":"images/combination3d_2977.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2977_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2977_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"B","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2977_q3","question_text":"How many separate pieces are shown in candidate B?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2977_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2977_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2977,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[2,0,0],[2,0,1],[2,0,2],[2,0,3],[3,0,0],[4,0,0],[4,0,1],[4,0,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":10},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,2,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[2,2,0],[2,2,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0]]],"total_cube_count":10}],"canvas_size":[568,441],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.5,"gravity_supported":true,"id":"combination3d_2978","image_path":"images/combination3d_2978.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2978_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2978_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2978_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2978_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,5","question_id":"combination3d_2978_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2978,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,2,0],[1,2,1],[2,0,0],[2,1,0],[2,2,0]],[[0,1,0],[0,1,1],[1,0,1],[1,1,1]],[[0,0,0],[1,0,0]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,2],[1,1,0],[2,0,0],[2,0,1],[2,0,2],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,2],[1,1,0],[1,2,0]],[[0,1,0],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":13}],"canvas_size":[569,469],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2979","image_path":"images/combination3d_2979.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2979_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2979_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2979_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2979_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2979_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2979,"target_cube_count":12,"target_cubes":[[0,2,0],[1,1,0],[1,1,1],[1,2,0],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[3,1,0],[3,1,1],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1]],[[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[1,2,2],[2,1,2]]],"total_cube_count":12},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[616,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2980","image_path":"images/combination3d_2980.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2980_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2980_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2980_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2980_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2980_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2980,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,0,1],[1,1,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,1],[1,1,1],[1,1,2],[2,0,1],[2,1,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9}],"canvas_size":[569,425],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2981","image_path":"images/combination3d_2981.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2981_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2981_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2981_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"9,3","question_id":"combination3d_2981_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2981_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2981,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]]],"total_cube_count":9},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":9},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[0,2,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":10}],"canvas_size":[614,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.39,"gravity_supported":true,"id":"combination3d_2982","image_path":"images/combination3d_2982.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2982_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2982_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2982_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2982_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,2","question_id":"combination3d_2982_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2982,"target_cube_count":9,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,2,0],[1,3,0],[1,4,0],[2,2,0],[2,3,0],[2,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,1,0],[1,1,1],[2,1,0],[3,1,0],[4,1,0],[5,0,0],[5,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0]],[[0,0,1],[1,0,1],[1,1,0],[1,1,1],[2,0,0],[2,0,1]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,5,0],[1,4,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,5,0],[1,3,0],[1,4,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[595,454],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2983","image_path":"images/combination3d_2983.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2983_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2983_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"C","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2983_q3","question_text":"How many separate pieces are shown in candidate C?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2983_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,3","question_id":"combination3d_2983_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2983,"target_cube_count":10,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,2,0],[0,3,0],[0,4,0],[0,5,0],[1,3,0],[1,3,1],[1,4,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,0],[1,3,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[0,0,4],[1,0,3],[1,0,4],[1,1,3],[1,1,4]]],"total_cube_count":15},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]],[[0,0,1],[1,0,1],[1,1,2],[2,0,0],[2,0,1],[2,0,2],[2,1,2],[2,1,3]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1]],[[0,0,0],[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,2],[1,0,3],[1,1,2],[1,1,3]]],"total_cube_count":14}],"canvas_size":[563,453],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2984","image_path":"images/combination3d_2984.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2984_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2984_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"B","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2984_q3","question_text":"Does candidate B have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,4","question_id":"combination3d_2984_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2984_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2984,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,0,3],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,0],[2,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[2,0,0]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":14},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,0,0]],[[0,0,0],[0,0,1]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1],[0,2,2],[1,0,1],[1,0,2],[1,1,1],[1,2,1],[2,0,0],[2,0,1]],[[0,0,0],[0,0,1],[0,1,0]]],"total_cube_count":15}],"canvas_size":[594,450],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.59,"gravity_supported":true,"id":"combination3d_2985","image_path":"images/combination3d_2985.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2985_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2985_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2985_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2985_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"15,3","question_id":"combination3d_2985_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2985,"target_cube_count":14,"target_cubes":[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,0,0],[1,0,1],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[1,4,0],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,1,1],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,1,0],[2,2,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,1],[0,1,2],[0,2,1]],[[0,0,0],[1,0,0],[2,0,0],[3,0,0]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[1,0,2],[1,1,0],[1,1,1],[1,2,0],[2,1,0]],[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[562,446],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2986","image_path":"images/combination3d_2986.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2986_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2986_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2986_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2986_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,4","question_id":"combination3d_2986_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2986,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,3,0],[1,1,0],[1,1,1],[1,2,0],[1,3,0],[2,0,0],[2,0,1],[2,1,0],[3,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[2,0,0]],[[0,0,0],[0,0,1],[0,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0],[2,0,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,3,0]],[[0,0,0],[1,0,0],[1,1,0],[1,1,1]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[0,1,3],[1,1,0],[2,1,0]],[[0,0,0],[0,1,0],[0,1,1],[1,1,1]]],"total_cube_count":11}],"canvas_size":[552,477],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2987","image_path":"images/combination3d_2987.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2987_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2987_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2987_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"11,3","question_id":"combination3d_2987_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2987_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2987,"target_cube_count":11,"target_cubes":[[0,2,0],[1,1,0],[1,2,0],[1,3,0],[1,3,1],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,2,0],[2,3,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[0,2,0],[1,1,1],[1,2,0],[1,2,1],[2,2,0]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1],[0,1,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[2,1,0],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,2],[0,1,3],[1,0,1],[1,1,0],[1,1,1],[1,1,2],[2,0,1]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[2,0,0]],[[0,0,0],[1,0,0]],[[0,0,1],[0,1,0],[0,1,1]]],"total_cube_count":12}],"canvas_size":[559,427],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.58,"gravity_supported":true,"id":"combination3d_2988","image_path":"images/combination3d_2988.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2988_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2988_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2988_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2988_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,4","question_id":"combination3d_2988_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2988,"target_cube_count":12,"target_cubes":[[0,1,0],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[3,0,0],[3,0,1],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,1],[2,1,2]],[[0,0,0],[0,1,0]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,1],[0,1,2],[0,2,1],[0,2,2],[0,3,1],[1,0,1],[1,1,1],[1,2,0],[1,2,1],[1,3,0],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2],[1,0,3],[1,1,2],[1,2,2]],[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[1,1,1]]],"total_cube_count":13}],"canvas_size":[618,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.55,"gravity_supported":true,"id":"combination3d_2989","image_path":"images/combination3d_2989.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2989_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2989_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2989_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"13,4","question_id":"combination3d_2989_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2989_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2989,"target_cube_count":13,"target_cubes":[[0,0,0],[0,0,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[2,0,0],[2,1,0],[2,1,1],[2,1,2]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,1],[0,1,2],[1,1,1],[1,1,2],[1,1,3],[2,1,3]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,3],[0,2,3],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[1,1,2],[1,1,3],[2,1,2]],[[0,0,0],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,2,0],[0,2,1],[1,1,0],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[3,0,0],[3,1,0]],[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[1,0,0]]],"total_cube_count":14}],"canvas_size":[558,467],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2990","image_path":"images/combination3d_2990.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2990_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2990_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2990_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2990_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,3","question_id":"combination3d_2990_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2990,"target_cube_count":13,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[1,1,1],[1,2,0],[1,2,1],[2,1,0],[2,2,0],[2,2,1],[3,1,0],[3,2,0],[4,0,0],[4,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,0],[0,2,1],[1,1,0]],[[0,0,0],[0,1,0]],[[0,0,1],[0,0,2],[1,0,0],[1,0,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,3,0],[1,0,0],[1,1,0],[1,2,0],[1,2,1],[1,3,0],[1,3,1],[2,3,0],[2,3,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0],[2,1,0]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":13}],"canvas_size":[605,420],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2991","image_path":"images/combination3d_2991.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2991_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2991_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2991_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2991_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,5","question_id":"combination3d_2991_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2991,"target_cube_count":12,"target_cubes":[[0,0,0],[1,0,0],[1,1,0],[2,0,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,2,0],[2,2,1],[3,1,0],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,1,0]],[[0,0,0],[0,1,0]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,1],[1,0,0],[1,0,1],[2,0,0],[2,0,1]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,1,0],[0,1,1],[0,1,2],[1,1,1],[1,1,2]]],"total_cube_count":9},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,1],[1,0,2]]],"total_cube_count":8}],"canvas_size":[550,452],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.35,"gravity_supported":true,"id":"combination3d_2992","image_path":"images/combination3d_2992.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_2992_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2992_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2992_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"8,3","question_id":"combination3d_2992_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2992_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2992,"target_cube_count":8,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[1,0,0],[1,1,0],[1,1,1],[1,1,2],[1,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0]],[[0,0,0],[0,1,0],[0,1,1],[0,2,0],[1,0,0],[1,1,0],[1,2,0]],[[0,0,0],[0,0,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,0,0],[0,1,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,1,0]],[[0,3,1],[1,0,0],[1,0,1],[1,1,1],[1,2,1],[1,3,1],[2,2,1],[2,3,1]]],"total_cube_count":11}],"canvas_size":[613,473],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.54,"gravity_supported":true,"id":"combination3d_2993","image_path":"images/combination3d_2993.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2993_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2993_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2993_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2993_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,4","question_id":"combination3d_2993_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2993,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,0,0],[2,1,0],[2,2,0],[3,0,0],[3,1,0],[3,1,1],[3,1,2],[3,2,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,0,1]],[[0,0,0],[1,0,0]],[[0,2,0],[0,2,1],[1,0,1],[1,1,1],[1,2,1]]],"total_cube_count":11},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1],[0,2,1],[0,3,1],[1,0,1],[1,1,0],[1,1,1],[1,2,1]],[[0,0,0],[1,0,0]]],"total_cube_count":11},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,0],[3,1,1]],[[0,0,0],[0,0,1]]],"total_cube_count":12}],"canvas_size":[602,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.47,"gravity_supported":true,"id":"combination3d_2994","image_path":"images/combination3d_2994.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"11","question_id":"combination3d_2994_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2994_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"A","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_2994_q3","question_text":"Does candidate A have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"C","question_id":"combination3d_2994_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"12,3","question_id":"combination3d_2994_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2994,"target_cube_count":11,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[2,1,0],[2,1,1],[3,1,0],[3,2,0],[3,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,2,1],[1,2,1],[1,2,2],[2,0,1],[2,1,1],[2,2,0],[2,2,1],[2,2,2]],[[0,0,0],[0,1,0]]],"total_cube_count":10},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,1],[1,0,0],[1,1,0],[1,1,1],[2,1,1],[2,2,1]],[[0,0,0],[1,0,0],[1,1,0]]],"total_cube_count":10},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[1,2,1],[2,0,0],[2,1,0]],[[0,0,0],[0,0,1]]],"total_cube_count":11}],"canvas_size":[594,428],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.43,"gravity_supported":true,"id":"combination3d_2995","image_path":"images/combination3d_2995.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"10","question_id":"combination3d_2995_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2995_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"A","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2995_q3","question_text":"How many separate pieces are shown in candidate A?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"D","question_id":"combination3d_2995_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"11,4","question_id":"combination3d_2995_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2995,"target_cube_count":10,"target_cubes":[[0,0,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,2,0],[2,0,0],[2,1,0],[3,1,0],[3,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0]],[[0,0,1],[0,1,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1],[2,1,1]],[[0,0,0],[0,1,0],[0,1,1]]],"total_cube_count":13},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[1,0,2],[1,1,0],[2,0,2]],[[0,0,0],[0,1,0],[1,0,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":13},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[1,1,1]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":14},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0]],[[0,0,0],[0,0,1],[0,0,2],[1,0,0]],[[0,0,0],[0,0,1]]],"total_cube_count":13}],"canvas_size":[574,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.62,"gravity_supported":true,"id":"combination3d_2996","image_path":"images/combination3d_2996.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"13","question_id":"combination3d_2996_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_2996_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2996_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2996_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"14,6","question_id":"combination3d_2996_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2996,"target_cube_count":13,"target_cubes":[[0,1,0],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,1,2],[2,1,3],[2,1,4],[3,1,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0]],[[0,0,0],[0,0,1],[1,0,1],[1,0,2]],[[0,0,0],[0,0,1]]],"total_cube_count":9},{"choice_label":"C","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[0,1,1],[1,0,0],[1,1,0],[2,0,0]],[[0,0,0],[1,0,0]]],"total_cube_count":10},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1],[1,2,1],[1,3,1]],[[0,0,0],[1,0,0]]],"total_cube_count":9}],"canvas_size":[556,480],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"A","dataset_version":"combination3d-5.0.0","difficulty_score":0.46,"gravity_supported":true,"id":"combination3d_2997","image_path":"images/combination3d_2997.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"9","question_id":"combination3d_2997_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"A","question_id":"combination3d_2997_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"2","question_id":"combination3d_2997_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"B","question_id":"combination3d_2997_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"10,5","question_id":"combination3d_2997_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2997,"target_cube_count":9,"target_cubes":[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[1,1,1],[2,0,0]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":15},{"choice_label":"B","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,1],[0,1,0],[0,1,1]],[[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,1,0]],[[0,0,0],[0,0,1],[0,0,2]]],"total_cube_count":14},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,1,0],[1,0,0],[1,1,0]],[[0,0,1],[0,1,0],[0,1,1],[0,1,2],[1,0,1],[1,1,2],[2,0,1],[3,0,1]],[[0,0,0],[1,0,0],[2,0,0]]],"total_cube_count":14},{"choice_label":"D","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[0,0,2],[0,1,2],[1,0,0]],[[0,0,0],[0,1,0]],[[0,0,0],[0,1,0],[0,2,0],[0,3,0],[0,3,1],[1,1,0],[1,2,0]]],"total_cube_count":14}],"canvas_size":[600,424],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"B","dataset_version":"combination3d-5.0.0","difficulty_score":0.66,"gravity_supported":true,"id":"combination3d_2998","image_path":"images/combination3d_2998.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"14","question_id":"combination3d_2998_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"B","question_id":"combination3d_2998_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"numeric","candidate_label":"D","difficulty_level":3,"ground_truth":"3","question_id":"combination3d_2998_q3","question_text":"How many separate pieces are shown in candidate D?","question_type":"candidate_piece_count"},{"answer_format":"numeric","difficulty_level":4,"ground_truth":"14,5","question_id":"combination3d_2998_q4","question_text":"Give the target's total cube count and maximum height along the vertical z-axis in layers as count,height.","question_type":"target_count_and_height"},{"answer_format":"short_text","difficulty_level":5,"ground_truth":"same shape, different angle","question_id":"combination3d_2998_q5","question_text":"If the correctly assembled structure were rotated 90 degrees around the vertical z-axis as a whole, would it be the 'same shape, different angle' or a 'different structure'?","question_type":"whole_group_rotation"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2998,"target_cube_count":14,"target_cubes":[[0,1,0],[0,1,1],[0,1,2],[0,1,3],[0,1,4],[1,0,0],[1,0,1],[1,0,2],[1,0,3],[1,1,0],[2,1,0],[2,1,1],[2,2,0],[2,2,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[0,2,0],[0,2,1],[1,0,0]],[[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,2,1],[1,1,0],[1,2,1]]],"total_cube_count":12},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,0],[0,1,0],[1,1,0]],[[0,1,0],[0,1,1],[0,2,1],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,2,1],[2,1,1]]],"total_cube_count":12},{"choice_label":"C","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1]]],"total_cube_count":12},{"choice_label":"D","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,0],[0,0,1],[1,0,0],[2,0,0],[2,1,0]],[[0,1,0],[0,2,0],[1,0,0],[1,0,1],[1,1,0],[2,1,0],[2,1,1],[2,2,1]]],"total_cube_count":13}],"canvas_size":[585,440],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"C","dataset_version":"combination3d-5.0.0","difficulty_score":0.51,"gravity_supported":true,"id":"combination3d_2999","image_path":"images/combination3d_2999.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"12","question_id":"combination3d_2999_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"C","question_id":"combination3d_2999_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"D","difficulty_level":3,"ground_truth":"no","question_id":"combination3d_2999_q3","question_text":"Does candidate D have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_2999_q4","question_text":"Which candidate has the correct cube count and piece shapes but would require tipping a piece onto a different face, rather than only spinning it around the vertical axis?","question_type":"requires_3d_tumble_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"13,3","question_id":"combination3d_2999_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":2999,"target_cube_count":12,"target_cubes":[[0,1,0],[0,1,1],[1,1,0],[2,1,0],[2,2,0],[3,1,0],[3,2,0],[4,0,0],[4,0,1],[4,1,0],[5,1,0],[5,1,1]],"vertical_axis":"z"}
{"candidates":[{"choice_label":"A","failure_reason":"wrong_count","is_valid_assembly":false,"pieces":[[[0,0,2],[1,0,0],[1,0,1],[1,0,2]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":9},{"choice_label":"B","failure_reason":"gap_or_overlap","is_valid_assembly":false,"pieces":[[[0,0,1],[0,0,2],[0,1,1],[1,1,0],[1,1,1]],[[0,0,0],[0,1,0],[1,1,0]]],"total_cube_count":8},{"choice_label":"C","failure_reason":"requires_3d_tumble","is_valid_assembly":false,"pieces":[[[0,0,0],[1,0,0],[2,0,0]],[[0,0,0],[0,1,0],[0,1,1]],[[0,0,0],[0,1,0]]],"total_cube_count":8},{"choice_label":"D","failure_reason":null,"is_valid_assembly":true,"pieces":[[[0,0,0],[0,0,1],[0,0,2]],[[0,1,0],[1,0,0],[1,1,0]],[[0,0,0],[0,1,0]]],"total_cube_count":8}],"canvas_size":[566,439],"coordinate_frame":"right_handed_xyz","correct_answer_choice":"D","dataset_version":"combination3d-5.0.0","difficulty_score":0.42,"gravity_supported":true,"id":"combination3d_3000","image_path":"images/combination3d_3000.png","permitted_piece_rotation_axes":["z"],"questions":[{"answer_format":"numeric","difficulty_level":1,"ground_truth":"8","question_id":"combination3d_3000_q1","question_text":"How many individual cubes make up the target structure?","question_type":"target_cube_count"},{"answer_format":"letter","difficulty_level":2,"ground_truth":"D","question_id":"combination3d_3000_q2","question_text":"Which set of pieces (A, B, C, or D) can be assembled using only translation and rotation around the vertical axis to exactly form the target structure? Answer with the letter.","question_type":"assembly3d_choice"},{"answer_format":"yes_no","candidate_label":"C","difficulty_level":3,"ground_truth":"yes","question_id":"combination3d_3000_q3","question_text":"Does candidate C have the same total number of cubes as the target? Answer yes or no.","question_type":"candidate_same_count"},{"answer_format":"letter","difficulty_level":4,"ground_truth":"A","question_id":"combination3d_3000_q4","question_text":"Which candidate has the wrong total number of cubes compared to the target?","question_type":"wrong_count_choice"},{"answer_format":"numeric","difficulty_level":5,"ground_truth":"9,4","question_id":"combination3d_3000_q5","question_text":"If one cube were added directly above a highest cube, what would the new total cube count and maximum height along the vertical z-axis be? Answer as count,height.","question_type":"add_cube_above_highest"}],"renderer_projection":"screen_x=0.8660254*(x-y); screen_y=0.5*(x+y)-z","seed":3000,"target_cube_count":8,"target_cubes":[[0,0,0],[0,1,0],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[2,0,0],[2,1,0]],"vertical_axis":"z"}